D006 / Pink / Review draft

Pink Paper Gateway Expression and Full Lifecycle 001

Terminology revised · evidence inherited

Pink Paper Gateway Expression and Full Lifecycle 001. Source pages 46-476. Nomenclature updated; historical equations, evidence limits and unresolved relationships retained.

MJ-PBMEF Pink Paper - Volume I
Gateway Expression, Bangel Construct Semantics, Command Normalization, and
R-to-N1-to-R2 Lifecycle
Michael Bangel - Author and Architect
August 2026


Contents
1
Executive gateway statement
2
2
Progressive expansion from MJ.23.r2
3
3
Token-by-token identification
4
4
Canonical execution order
5
5
R, R1, N1, R2, and final output
6
6
Bangel construct dictionary
7
7
Full declarative gateway example
8
8
Verification of the full corpus
9
Document control
Project
MJ: Physics Based Measurement Engineering Framework
Project ID
MJ-PBMEF-001
Source build
MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE
Document ID
MJ-PBMEF-PINK-PAPER-001/VOL-I
Author and architect
Michael Bangel
Status
FOUNDER_REVIEW_CANDIDATE_PENDING_FREEZE
Scope
Gateway expression and syntax semantics for the full Day-0 R4
source model.
Claims ceiling
This document is a private pre-Day-0 review and verification candidate. It authenticates no pri-
vate key and creates no physical validation, physical operation authority, product certification,
external regulatory authority, production deployment, financial-product launch, token issuance,
AI integration, or physical-coordinate approval. Formula pages distinguish mathematical validity,
reference implementation, simulation, measured evidence, authority, and execution.
1


Chapter 1
Executive gateway statement
The Pink Paper is a verification-focused declarative pathway specification. It uses the founder-supplied
expression as a source-provenance object, then separates lexical order from canonical execution or-
der. The paper shows how each formula, manifestation, object, product, and white paper enters the MJ
framework without confusing representation, measurement, authority, or execution.
Founder source literal
{hagelaohrbcoe.48383829}.M3.act.MJ.23.r2.exe.r1.confirm.G123.reconcile.Bangel.begin
2


Chapter 2
Progressive expansion from MJ.23.r2
Stage
Expression
Interpretation
1
MJ.23.r2
Profile/state seed
2
MJ.23.r2.exe
Adds requested execution verb
3
MJ.23.r2.exe.r1.confirm
Adds transition and confirmation
4
MJ.23.r2.exe.r1.confirm.G123.reconcile
Adds generational reconciliation
5
MJ.23.r2.exe.r1.confirm.G123.reconcile.Bangel.begin
Adds language start directive
6
M3.act.MJ.23.r2.exe.r1.confirm.G123.reconcile.Bangel.begin
Adds bounded routing and requested
action
7
{hagelaohrbcoe.48383829}.M3.act.MJ.23.r2.exe.r1.confirm.G123.reconcile.Bangel.begin
Adds opaque request envelope and
exact front-end allocation seed
Canonical normalization rule
The raw dotted sequence is preserved as human-authored provenance. It is not executed left-to-
right. Canonical execution begins with HumanPurpose and MJ root scope, enters Bangel.begin,
recovers semantics through Elsa, constructs JP representations, passes MK physics classification,
JO verification, R1 evidence transition, N1 prediction-first allocation, applicable family evidence,
M3 routing, Mermaid/Shiva reconciliation, MJ permit decision, JO execution, and final R2 evi-
dence.
3


Chapter 3
Token-by-token identification
Token
Exact meaning and boundary
{hagelaohrbcoe.48383829}
Request envelope containing an opaque request identifier and exact ratio 48,383,829 /
100,000,000. It is not a physical coordinate, probability of truth, or permit.
M3
Mary/M3 bounded routing and allocation participant. M3 cannot mint authority.
act
Requested effect verb. It remains a request until all gates pass.
MJ
Framework root and final bounded decision authority.
23
Typed reference requiring explicit context. In the mass branch it means 23 mg pre-
observational floor; it is not interchangeable with a profile label.
r2
Requested or referenced living-static state; cannot precede validated R1 transition in
canonical execution.
exe
Execution directive; denied until JO proof, safety, authority, and MJ permit pass.
r1
Unidentified transitionary phase.
confirm
Evidence-confirmation statement; confirmation is evidence-scoped, not self-
authorizing.
G123
Generational resource/memory/reconciliation context.
reconcile
Conservation, accounting, evidence, and residual closure.
Bangel
Typed language and declaration plane inside MJ.
begin
Start directive for parsing and admission; no external effect.
4


Chapter 4
Canonical execution order
HumanPurpose
-> MJ.root
-> Bangel.begin
-> Elsa.recover
-> JP.represent
-> MK.classify
-> JO.verify
-> R1.transition
-> N1.predict_and_preallocate
-> Angels/Bellatrix/Sister/EVE.evidence
-> M3.route
-> Mermaid.reconcile
-> Shiva.when_capital_applies
-> MJ.permit
-> JO.execute
-> R2.output_receipt
5


Chapter 5
R, R1, N1, R2, and final output
Lifecycle state
Definition
R / R0
Initial purpose, command, variables, authority context, and unresolved inputs.
R1
Unidentified transitionary phase. Missing or disputed evidence remains typed and can-
not become zero.
N1
First prediction-based allocation node. It receives validated logical allocation context,
not a physical-coordinate approval.
R2
Immutable living-static representation after scoped validation.
Final output
JO evidence receipt containing result, scope, roots, participants, uncertainty, holds, cor-
rections, and MJ permit state.
6


Chapter 6
Bangel construct dictionary
Construct
Definition
Module
A bounded compilation or specification unit grouping related declarations and defini-
tions.
Namespace
A stable identity domain preventing collisions among family, formula, product, and object
names.
Import
An explicit dependency edge. Imports confer no authority and must preserve source di-
gest and version.
Declaration
A named commitment that an object, formula, participant, type, or function exists in the
source model.
Definition
The exact normative meaning, not merely a label.
Capability
A bounded action or representation class available only within current authority and evi-
dence.
Participant
A family manifestation that contributes a non-substitutable role.
Relationship
A typed edge among participants, objects, resources, evidence, or decisions.
Function
A deterministic transformation from typed inputs to typed outputs or disposition.
Expression
A formula, boolean predicate, path, or compositional object.
Statement
A normative or executable sentence in the language.
Measurement
An observation with quantity kind, native unit, boundary, time, instrument, calibration,
and uncertainty.
Constraint
A non-negotiable predicate such as UNKNOWN != 0 or unit compatibility.
Annotation
Metadata binding IDs, provenance, evidence ceilings, authorship, or review status.
Directive
A controlled instruction such as begin, verify, hold, reconcile, or deny.
Block
A scoped set of declarations, definitions, directives, and invariants.
Literal
An exact source value, string, ratio, unit-bearing number, or symbolic constant.
Reference
A digest-bound pointer to another artifact, formula, object, receipt, or revision.
Type
A quantity, state, participant, object, evidence, authority, or disposition class.
Attribute
A named property such as state, scope, revision, evidence ceiling, or permit classifica-
tion.
7


Chapter 7
Full declarative gateway example
module MJ.PBMEF.Gateway {
namespace MJ.PBMEF.Command.Day0
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
import MJ.PBMEF.Family
@source_literal(
"{hagelaohrbcoe.48383829}."
"M3.act.MJ.23.r2.exe.r1.confirm."
"G123.reconcile.Bangel.begin"
)
declaration request : CommandEnvelope
definition request.id = "hagelaohrbcoe"
definition request.front_end_seed = exact_ratio(48383829, 100000000)
constraint UNKNOWN != 0
constraint R1 precedes validated R2
constraint MJ.permit precedes act and exe
constraint M3 cannot mint authority
block lifecycle {
directive Bangel.begin
function Elsa.recover(request.purpose)
reference JP.represent(all_applicable_formulas)
statement MK.classify_physics_applicability
statement JO.verify_units_boundaries_evidence
statement R0 -> R1
capability N1.predict_and_preallocate
relationship applicable_families.provide_evidence
directive M3.route
directive Mermaid.reconcile
directive Shiva.analyze when capital_applies
directive MJ.permit
directive JO.execute
statement R1 --validated--> R2
}
}
8


Chapter 8
Verification of the full corpus
This Pink Paper binds the gateway to 21 family manifestations, 39 governed objects, 28 products,
145 formulas, and 61 registered white papers. The remaining volumes enumerate each item and
state how it enters the gateway, what it may express, what evidence it requires, and what authority it
cannot create.
9


MJ-PBMEF Pink Paper - Volume II
Formula Gateway Bindings F-001 through F-050
Michael Bangel - Author and Architect
August 2026


Contents
1
Verification method
5
2
F-001 - R1 transition
6
2.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3
F-002 - R2 transition
8
3.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
3.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
4
F-003 - Unknown invariant
10
4.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
4.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
5
F-004 - Mass inflection
12
5.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
5.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
6
F-005 - Noise smoothing
14
6.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
6.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
7
F-006 - Trend estimator
16
7.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
7.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
8
F-007 - Anti-spike gate
18
8.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
8.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
9
F-008 - Prediction gain
20
9.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
9.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
10F-009 - Covariance update
22
10.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
10.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
11F-010 - Shadow depth
24
11.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
11.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
12F-011 - Shadow growth rate
26
12.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
12.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
13F-012 - Front-end allocation
28
13.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
1


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
13.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
14F-013 - Front-end reserve
30
14.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
14.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
15F-014 - Bounded allocation update
32
15.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
15.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
16F-015 - Request memory
34
16.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
16.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
17F-016 - Memory preallocation
36
17.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
17.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
18F-017 - Hard flush
38
18.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
18.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
19F-018 - Charge balance
40
19.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
19.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
20F-019 - Capacitor energy
42
20.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
20.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
21F-020 - General stored energy
44
21.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
21.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
22F-021 - Energy balance
46
22.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
22.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
23F-022 - Mass balance
48
23.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
23.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
24F-023 - EVE screen balance
50
24.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
24.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
25F-024 - EVE evaporation
52
25.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
25.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
26F-025 - Upward force
54
26.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
26.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
27F-026 - Coordinate mapping
56
27.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
27.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
28F-027 - Sister physical umbrella count
58
28.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
28.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
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PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
29F-028 - Byte balance
60
29.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
29.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
30F-029 - Residual consequence
62
30.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
30.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
31F-030 - Protected liquidity
64
31.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
31.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
32F-031 - Investable surplus
66
32.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
32.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
33F-032 - Risk-capital ceiling
68
33.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
33.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
34F-033 - Portfolio concentration
70
34.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
34.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
35F-034 - Portfolio variance
72
35.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
35.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
36F-035 - Capital friction
74
36.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
36.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
37F-036 - Opportunity lower bound
76
37.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
37.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
38F-037 - Abundance objective
78
38.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
38.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
39F-038 - SHIVAS eligible value
80
39.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
39.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
40F-039 - SHIVAS ceiling
82
40.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
40.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
41F-040 - MK state model
84
41.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
41.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
42F-041 - Dimensional integrity
86
42.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
42.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
43F-042 - Conservation residual
88
43.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
43.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
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PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
44F-043 - Pearl simulation ellipsoid volume
90
44.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
44.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
45F-044 - Pearl simulation surface-area approximation
92
45.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
45.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
46F-045 - Pearl simulation exposure ratio
94
46.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
46.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
47F-046 - Pearl simulation capacity slack
96
47.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
47.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
48F-047 - Pearl simulation saturation ratio
98
48.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
48.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
49F-048 - Pearl simulation object count
100
49.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
49.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
50F-049 - Pearl simulation accounting balance
102
50.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
50.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
51F-050 - Pearl simulated transfer opportunity
104
51.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
51.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Document control
Project
MJ: Physics Based Measurement Engineering Framework
Project ID
MJ-PBMEF-001
Source build
MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE
Document ID
MJ-PBMEF-PINK-PAPER-001/VOL-II
Author and architect
Michael Bangel
Status
FOUNDER_REVIEW_CANDIDATE_PENDING_FREEZE
Scope
Formula-level gateway bindings for F-001 through F-050.
Claims ceiling
This document is a private pre-Day-0 review and verification candidate. It authenticates no pri-
vate key and creates no physical validation, physical operation authority, product certification,
external regulatory authority, production deployment, financial-product launch, token issuance,
AI integration, or physical-coordinate approval. Formula pages distinguish mathematical validity,
reference implementation, simulation, measured evidence, authority, and execution.
Page 4 of 105


Chapter 1
Verification method
Each formula receives the same twenty-construct Bangel identity, a gateway-stage assignment, a life-
cycle example, and explicit evidence and ethics boundaries. The repetitive structure is intentional: it
allows formula-by-formula founder review and later automated completeness checking.
5


Chapter 2
F-001 - R1 transition
Exact expression
R0 -> R1
Meaning. R1 is the unidentified transitionary phase.
Bound manifestations. Bangel, JP, JO
Gateway stage. R0/R1/R2 state transition and evidence classification
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_001
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO
Declaration
formula F-001 ’R1 transition’
Definition
R1 is the unidentified transitionary phase.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, JP, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R0/R1/R2 state transition and evidence classification
Expression
R0 -> R1
Statement
When typed inputs and evidence gates pass, evaluate F-001; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: state; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-001’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-001); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-001 and applicable family/product/representation white papers
Type
state
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R0/R1/R2 state transition and evidence classification’; physical_validation=false; authority=false
2.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_001 : Formula<state>
definition "R1 is the unidentified transitionary phase."
expression `R0 -> R1`
participants ["Bangel", "JP", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
6


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
2.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-001 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 7 of 105


Chapter 3
F-002 - R2 transition
Exact expression
R1 --validated--> R2
Meaning. R2 is the immutable living static representation.
Bound manifestations. JP, MK, JO
Gateway stage. R0/R1/R2 state transition and evidence classification
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_002
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-002 ’R2 transition’
Definition
R2 is the immutable living static representation.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R0/R1/R2 state transition and evidence classification
Expression
R1 –validated–> R2
Statement
When typed inputs and evidence gates pass, evaluate F-002; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: state; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-002’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-002); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-002 and applicable family/product/representation white papers
Type
state
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R0/R1/R2 state transition and evidence classification’; physical_validation=false; authority=false
3.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_002 : Formula<state>
definition "R2 is the immutable living static representation."
expression `R1 --validated--> R2`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
8


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
3.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-002 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 9 of 105


Chapter 4
F-003 - Unknown invariant
Exact expression
UNKNOWN != 0
Meaning. Unknown may not coerce to zero, pass, harmlessness, or permission.
Bound manifestations. Bangel, JO, WATER
Gateway stage. R0/R1/R2 state transition and evidence classification
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_003
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.WATER
Declaration
formula F-003 ’Unknown invariant’
Definition
Unknown may not coerce to zero, pass, harmlessness, or permission.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, JO, WATER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R0/R1/R2 state transition and evidence classification
Expression
UNKNOWN != 0
Statement
When typed inputs and evidence gates pass, evaluate F-003; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-003’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-003); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-003 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R0/R1/R2 state transition and evidence classification’; physical_validation=false; authority=false
4.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_003 : Formula<logical>
definition "Unknown may not coerce to zero, pass, harmlessness, or permission."
expression `UNKNOWN != 0`
participants ["Bangel", "JO", "WATER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
10


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
4.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-003 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 11 of 105


Chapter 5
F-004 - Mass inflection
Exact expression
m_floor = 23 mg
Meaning. Pre-observational model floor, not a universal minimum or product mass.
Bound manifestations. JP, MK, EVE, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_004
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-004 ’Mass inflection’
Definition
Pre-observational model floor, not a universal minimum or product mass.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
m_floor = 23 mg
Statement
When typed inputs and evidence gates pass, evaluate F-004; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-004’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-004); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
23
Reference
pathways/FORMULA-REGISTER.json#F-004 and applicable family/product/representation white papers
Type
mass
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
5.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_004 : Formula<mass>
definition "Pre-observational model floor, not a universal minimum or product mass."
expression `m_floor = 23 mg`
participants ["JP", "MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
12


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
5.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-004 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 13 of 105


Chapter 6
F-005 - Noise smoothing
Exact expression
n_bar[t] = 0.9*n_bar[t-1] + 0.1*n[t]
Meaning. Drip-level smoothing.
Bound manifestations. SISTER, JO, MK
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_005
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MK
Declaration
formula F-005 ’Noise smoothing’
Definition
Drip-level smoothing.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SISTER, JO, MK
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
n_bar[t] = 0.9*n_bar[t-1] + 0.1*n[t]
Statement
When typed inputs and evidence gates pass, evaluate F-005; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimensionless; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-005’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-005); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.9, 1, 0.1
Reference
pathways/FORMULA-REGISTER.json#F-005 and applicable family/product/representation white papers
Type
dimensionless
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
6.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_005 : Formula<dimensionless>
definition "Drip-level smoothing."
expression `n_bar[t] = 0.9*n_bar[t-1] + 0.1*n[t]`
participants ["SISTER", "JO", "MK"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
14


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
6.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-005 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 15 of 105


Chapter 7
F-006 - Trend estimator
Exact expression
n_dot[t] = (2/3)*n_dot[t-1] + (1/3)*(n_bar[t]-n_bar[t-1])/dt
Meaning. One-third trend update.
Bound manifestations. SISTER, JO, MK
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_006
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MK
Declaration
formula F-006 ’Trend estimator’
Definition
One-third trend update.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, JO, MK
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
n_dot[t] = (2/3)*n_dot[t-1] + (1/3)*(n_bar[t]-n_bar[t-1])/dt
Statement
When typed inputs and evidence gates pass, evaluate F-006; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: 1/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-006’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-006); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2, 3, 1
Reference
pathways/FORMULA-REGISTER.json#F-006 and applicable family/product/representation white papers
Type
1/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
7.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_006 : Formula<1/time>
definition "One-third trend update."
expression `n_dot[t] = (2/3)*n_dot[t-1] + (1/3)*(n_bar[t]-n_bar[t-1])/dt`
participants ["SISTER", "JO", "MK"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
16


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
7.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-006 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 17 of 105


Chapter 8
F-007 - Anti-spike gate
Exact expression
support>=3 of 5 AND 3 qualified windows
Meaning. Single spike cannot trigger full reweighting.
Bound manifestations. SISTER, ANGELS, JO
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_007
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.JO
Declaration
formula F-007 ’Anti-spike gate’
Definition
Single spike cannot trigger full reweighting.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
SISTER, ANGELS, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
support>=3 of 5 AND 3 qualified windows
Statement
When typed inputs and evidence gates pass, evaluate F-007; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-007’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-007); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
3, 5
Reference
pathways/FORMULA-REGISTER.json#F-007 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
8.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_007 : Formula<logical>
definition "Single spike cannot trigger full reweighting."
expression `support>=3 of 5 AND 3 qualified windows`
participants ["SISTER", "ANGELS", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
18


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
8.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-007 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 19 of 105


Chapter 9
F-008 - Prediction gain
Exact expression
g_i = 0.1*(2/3)^(i-1)
Meaning. Prediction influence decays across the nine-node path.
Bound manifestations. JP, SISTER, JO
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_008
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.JO
Declaration
formula F-008 ’Prediction gain’
Definition
Prediction influence decays across the nine-node path.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, SISTER, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
g_i = 0.1*(2/3)^(i-1)
Statement
When typed inputs and evidence gates pass, evaluate F-008; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimensionless; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-008’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-008); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.1, 2, 3, 1
Reference
pathways/FORMULA-REGISTER.json#F-008 and applicable family/product/representation white papers
Type
dimensionless
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
9.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_008 : Formula<dimensionless>
definition "Prediction influence decays across the nine-node path."
expression `g_i = 0.1*(2/3)^(i-1)`
participants ["JP", "SISTER", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
20


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
9.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-008 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 21 of 105


Chapter 10
F-009 - Covariance update
Exact expression
Sigma_next = 0.9*Sigma_prev + 0.1*e*e^T
Meaning. Positive-semidefinite sequential covariance.
Bound manifestations. JP, MK, JO
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_009
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-009 ’Covariance update’
Definition
Positive-semidefinite sequential covariance.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
Sigma_next = 0.9*Sigma_prev + 0.1*e*e^T
Statement
When typed inputs and evidence gates pass, evaluate F-009; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: normalized^2; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-009’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-009); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.9, 0.1
Reference
pathways/FORMULA-REGISTER.json#F-009 and applicable family/product/representation white papers
Type
normalized^2
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
10.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_009 : Formula<normalized^2>
definition "Positive-semidefinite sequential covariance."
expression `Sigma_next = 0.9*Sigma_prev + 0.1*e*e^T`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
22


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
10.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-009 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 23 of 105


Chapter 11
F-010 - Shadow depth
Exact expression
H = sqrt(lambda_max(Sigma))
Meaning. Uncertainty depth.
Bound manifestations. MK, SISTER, EVE
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_010
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE
Declaration
formula F-010 ’Shadow depth’
Definition
Uncertainty depth.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, SISTER, EVE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
H = sqrt(lambda_max(Sigma))
Statement
When typed inputs and evidence gates pass, evaluate F-010; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: normalized; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-010’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-010); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-010 and applicable family/product/representation white papers
Type
normalized
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
11.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_010 : Formula<normalized>
definition "Uncertainty depth."
expression `H = sqrt(lambda_max(Sigma))`
participants ["MK", "SISTER", "EVE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
24


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
11.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-010 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 25 of 105


Chapter 12
F-011 - Shadow growth rate
Exact expression
v_shadow = (H_next-H_prev)/dt
Meaning. Rate of uncertainty expansion or resolution.
Bound manifestations. MK, SISTER, JO
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_011
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.JO
Declaration
formula F-011 ’Shadow growth rate’
Definition
Rate of uncertainty expansion or resolution.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, SISTER, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
v_shadow = (H_next-H_prev)/dt
Statement
When typed inputs and evidence gates pass, evaluate F-011; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: normalized/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-011’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-011); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-011 and applicable family/product/representation white papers
Type
normalized/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
12.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_011 : Formula<normalized/time>
definition "Rate of uncertainty expansion or resolution."
expression `v_shadow = (H_next-H_prev)/dt`
participants ["MK", "SISTER", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
26


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
12.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-011 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 27 of 105


Chapter 13
F-012 - Front-end allocation
Exact expression
a0 = 48383829/100000000
Meaning. Exact initial N1 logical allocation.
Bound manifestations. Bangel, JP, JO, M3
Gateway stage. N1 prediction-first allocation, M3 routing, and G123 reconciliation
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_012
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-012 ’Front-end allocation’
Definition
Exact initial N1 logical allocation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
Bangel, JP, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
N1 prediction-first allocation, M3 routing, and G123 reconciliation
Expression
a0 = 48383829/100000000
Statement
When typed inputs and evidence gates pass, evaluate F-012; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-012’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-012); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
48383829, 100000000
Reference
pathways/FORMULA-REGISTER.json#F-012 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’N1 prediction-first allocation, M3 routing, and G123 reconciliation’; physical_validation=false; author-
ity=false
13.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_012 : Formula<ratio>
definition "Exact initial N1 logical allocation."
expression `a0 = 48383829/100000000`
participants ["Bangel", "JP", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
28


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
13.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-012 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 29 of 105


Chapter 14
F-013 - Front-end reserve
Exact expression
r0 = 51616171/100000000
Meaning. Exact logical reserve.
Bound manifestations. JP, JO, M3
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_013
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-013 ’Front-end reserve’
Definition
Exact logical reserve.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r0 = 51616171/100000000
Statement
When typed inputs and evidence gates pass, evaluate F-013; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-013’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-013); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
51616171, 100000000
Reference
pathways/FORMULA-REGISTER.json#F-013 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
14.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_013 : Formula<ratio>
definition "Exact logical reserve."
expression `r0 = 51616171/100000000`
participants ["JP", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
30


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
14.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-013 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 31 of 105


Chapter 15
F-014 - Bounded allocation update
Exact expression
w_next = projection((2/3)w + (1/3)w_target)
Meaning. Nonnegative, sum-to-one, per-step change <=0.1.
Bound manifestations. JP, JO, M3
Gateway stage. N1 prediction-first allocation, M3 routing, and G123 reconciliation
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_014
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-014 ’Bounded allocation update’
Definition
Nonnegative, sum-to-one, per-step change <=0.1.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
N1 prediction-first allocation, M3 routing, and G123 reconciliation
Expression
w_next = projection((2/3)w + (1/3)w_target)
Statement
When typed inputs and evidence gates pass, evaluate F-014; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio vector; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-014’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-014); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2, 3, 1
Reference
pathways/FORMULA-REGISTER.json#F-014 and applicable family/product/representation white papers
Type
ratio vector
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’N1 prediction-first allocation, M3 routing, and G123 reconciliation’; physical_validation=false; author-
ity=false
15.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_014 : Formula<ratio vector>
definition "Nonnegative, sum-to-one, per-step change <=0.1."
expression `w_next = projection((2/3)w + (1/3)w_target)`
participants ["JP", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
32


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
15.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-014 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 33 of 105


Chapter 16
F-015 - Request memory
Exact expression
M_request = lambda_hat * bytes_per_request * latency_hat
Meaning. Predicted request memory.
Bound manifestations. JO, M3, MJOS
Gateway stage. N1 prediction-first allocation, M3 routing, and G123 reconciliation
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_015
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MJOS
Declaration
formula F-015 ’Request memory’
Definition
Predicted request memory.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, MJOS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
N1 prediction-first allocation, M3 routing, and G123 reconciliation
Expression
M_request = lambda_hat * bytes_per_request * latency_hat
Statement
When typed inputs and evidence gates pass, evaluate F-015; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: bytes; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-015’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-015); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-015 and applicable family/product/representation white papers
Type
bytes
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’N1 prediction-first allocation, M3 routing, and G123 reconciliation’; physical_validation=false; author-
ity=false
16.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_015 : Formula<bytes>
definition "Predicted request memory."
expression `M_request = lambda_hat * bytes_per_request * latency_hat`
participants ["JO", "M3", "MJOS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
34


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
16.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-015 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 35 of 105


Chapter 17
F-016 - Memory preallocation
Exact expression
M_pre = M_request + M_sync + M_residual + M_evidence + M_headroom
Meaning. Preallocate before reserve exhaustion.
Bound manifestations. JO, M3, SISTER
Gateway stage. N1 prediction-first allocation, M3 routing, and G123 reconciliation
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_016
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.SISTER
Declaration
formula F-016 ’Memory preallocation’
Definition
Preallocate before reserve exhaustion.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
N1 prediction-first allocation, M3 routing, and G123 reconciliation
Expression
M_pre = M_request + M_sync + M_residual + M_evidence + M_headroom
Statement
When typed inputs and evidence gates pass, evaluate F-016; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: bytes; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-016’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-016); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-016 and applicable family/product/representation white papers
Type
bytes
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’N1 prediction-first allocation, M3 routing, and G123 reconciliation’; physical_validation=false; author-
ity=false
17.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_016 : Formula<bytes>
definition "Preallocate before reserve exhaustion."
expression `M_pre = M_request + M_sync + M_residual + M_evidence + M_headroom`
participants ["JO", "M3", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
36


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
17.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-016 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 37 of 105


Chapter 18
F-017 - Hard flush
Exact expression
QUIESCE -> SEAL -> CHECKPOINT -> DETACH -> RECLAIM
Meaning. No silent deletion or uncleared reuse.
Bound manifestations. JO, M3, MJOS
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.foundation.state_noise_allocation_memory
Namespace
MJ.PBMEF.foundation.state_noise_allocation_memory.F_017
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MJOS
Declaration
formula F-017 ’Hard flush’
Definition
No silent deletion or uncleared reuse.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, MJOS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
QUIESCE -> SEAL -> CHECKPOINT -> DETACH -> RECLAIM
Statement
When typed inputs and evidence gates pass, evaluate F-017; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: state sequence; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-017’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-017); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-017 and applicable family/product/representation white papers
Type
state sequence
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
18.1 Gateway life-cycle example
module MJ.PBMEF.foundation.state_noise_allocation_memory {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_017 : Formula<state sequence>
definition "No silent deletion or uncleared reuse."
expression `QUIESCE -> SEAL -> CHECKPOINT -> DETACH -> RECLAIM`
participants ["JO", "M3", "MJOS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
38


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
18.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-017 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 39 of 105


Chapter 19
F-018 - Charge balance
Exact expression
dQ/dt = I_intake - I_leak - I_release
Meaning. Static-intake charge accounting.
Bound manifestations. JP, MK, EVE, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_018
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-018 ’Charge balance’
Definition
Static-intake charge accounting.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
dQ/dt = I_intake - I_leak - I_release
Statement
When typed inputs and evidence gates pass, evaluate F-018; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: charge/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-018’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-018); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-018 and applicable family/product/representation white papers
Type
charge/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
19.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_018 : Formula<charge/time>
definition "Static-intake charge accounting."
expression `dQ/dt = I_intake - I_leak - I_release`
participants ["JP", "MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
40


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
19.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-018 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 41 of 105


Chapter 20
F-019 - Capacitor energy
Exact expression
E = 0.5*C*V^2
Meaning. Valid only for evidenced constant capacitance.
Bound manifestations. JP, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_019
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-019 ’Capacitor energy’
Definition
Valid only for evidenced constant capacitance.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
E = 0.5*C*V^2
Statement
When typed inputs and evidence gates pass, evaluate F-019; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: energy; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-019’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-019); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.5, 2
Reference
pathways/FORMULA-REGISTER.json#F-019 and applicable family/product/representation white papers
Type
energy
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
20.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_019 : Formula<energy>
definition "Valid only for evidenced constant capacitance."
expression `E = 0.5*C*V^2`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
42


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
20.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-019 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 43 of 105


Chapter 21
F-020 - General stored energy
Exact expression
E = integral V(q)dq
Meaning. General charge-storage energy.
Bound manifestations. JP, MK
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_020
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK
Declaration
formula F-020 ’General stored energy’
Definition
General charge-storage energy.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
E = integral V(q)dq
Statement
When typed inputs and evidence gates pass, evaluate F-020; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: energy; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-020’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-020); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-020 and applicable family/product/representation white papers
Type
energy
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
21.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_020 : Formula<energy>
definition "General charge-storage energy."
expression `E = integral V(q)dq`
participants ["JP", "MK"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
44


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
21.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-020 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 45 of 105


Chapter 22
F-021 - Energy balance
Exact expression
r_E = E_in - DeltaE_storage - E_delivered - E_containment - E_loss
Meaning. Energy residual must be inside uncertainty.
Bound manifestations. MK, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_021
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-021 ’Energy balance’
Definition
Energy residual must be inside uncertainty.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r_E = E_in - DeltaE_storage - E_delivered - E_containment - E_loss
Statement
When typed inputs and evidence gates pass, evaluate F-021; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: energy; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-021’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-021); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-021 and applicable family/product/representation white papers
Type
energy
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
22.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_021 : Formula<energy>
definition "Energy residual must be inside uncertainty."
expression `r_E = E_in - DeltaE_storage - E_delivered - E_containment - E_loss`
participants ["MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
46


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
22.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-021 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 47 of 105


Chapter 23
F-022 - Mass balance
Exact expression
r_M = M_initial + M_inputs - M_final - M_outputs
Meaning. Physical mass conservation.
Bound manifestations. MK, EVE, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_022
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-022 ’Mass balance’
Definition
Physical mass conservation.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r_M = M_initial + M_inputs - M_final - M_outputs
Statement
When typed inputs and evidence gates pass, evaluate F-022; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-022’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-022); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-022 and applicable family/product/representation white papers
Type
mass
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
23.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_022 : Formula<mass>
definition "Physical mass conservation."
expression `r_M = M_initial + M_inputs - M_final - M_outputs`
participants ["MK", "EVE", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
48


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
23.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-022 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 49 of 105


Chapter 24
F-023 - EVE screen balance
Exact expression
M_screen_in = M_captured + M_passed + M_retained + r_screen
Meaning. Screen capture never assumes perfect retention.
Bound manifestations. EVE, MK, JO, MERMAID
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_023
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-023 ’EVE screen balance’
Definition
Screen capture never assumes perfect retention.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
EVE, MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
M_screen_in = M_captured + M_passed + M_retained + r_screen
Statement
When typed inputs and evidence gates pass, evaluate F-023; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-023’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-023); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-023 and applicable family/product/representation white papers
Type
mass
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
24.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_023 : Formula<mass>
definition "Screen capture never assumes perfect retention."
expression `M_screen_in = M_captured + M_passed + M_retained + r_screen`
participants ["EVE", "MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
50


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
24.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-023 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 51 of 105


Chapter 25
F-024 - EVE evaporation
Exact expression
M_evap = integral integral J_m dA dt
Meaning. Evaporative mass from flux across area and time.
Bound manifestations. EVE, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_024
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-024 ’EVE evaporation’
Definition
Evaporative mass from flux across area and time.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
EVE, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
M_evap = integral integral J_m dA dt
Statement
When typed inputs and evidence gates pass, evaluate F-024; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-024’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-024); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-024 and applicable family/product/representation white papers
Type
mass
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
25.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_024 : Formula<mass>
definition "Evaporative mass from flux across area and time."
expression `M_evap = integral integral J_m dA dt`
participants ["EVE", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
52


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
25.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-024 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 53 of 105


Chapter 26
F-025 - Upward force
Exact expression
F_z = qE_z + F_b - mg - D_z - F_contact - F_adhesion
Meaning. Upward motion requires positive conservative lower bound.
Bound manifestations. MK, EVE, BELLE
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_025
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.BELLE
Declaration
formula F-025 ’Upward force’
Definition
Upward motion requires positive conservative lower bound.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, BELLE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
F_z = qE_z + F_b - mg - D_z - F_contact - F_adhesion
Statement
When typed inputs and evidence gates pass, evaluate F-025; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: force; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-025’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-025); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-025 and applicable family/product/representation white papers
Type
force
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
26.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_025 : Formula<force>
definition "Upward motion requires positive conservative lower bound."
expression `F_z = qE_z + F_b - mg - D_z - F_contact - F_adhesion`
participants ["MK", "EVE", "BELLE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
54


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
26.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-025 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 55 of 105


Chapter 27
F-026 - Coordinate mapping
Exact expression
p_P(x,y,z)=o_P+x*a_P+y*b_P+z*c_P
Meaning. Normalized topology to profile physical coordinates.
Bound manifestations. JP, MK, BELLE, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_026
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.BELLE, MJ.PBMEF.Family.JO
Declaration
formula F-026 ’Coordinate mapping’
Definition
Normalized topology to profile physical coordinates.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, BELLE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
p_P(x,y,z)=o_P+x*a_P+y*b_P+z*c_P
Statement
When typed inputs and evidence gates pass, evaluate F-026; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length vector; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-026’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-026); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-026 and applicable family/product/representation white papers
Type
length vector
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
27.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_026 : Formula<length vector>
definition "Normalized topology to profile physical coordinates."
expression `p_P(x,y,z)=o_P+x*a_P+y*b_P+z*c_P`
participants ["JP", "MK", "BELLE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
56


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
27.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-026 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 57 of 105


Chapter 28
F-027 - Sister physical umbrella count
Exact expression
N_U = max_k ceil(E_k/((1-h_k)*C_Uk))
Meaning. Canonical pre-Pearl physical containment count; requires measured profile-specific capacity
and headroom.
Bound manifestations. SISTER, MK, JO, M3
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_027
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-027 ’Sister physical umbrella count’
Definition
Canonical pre-Pearl physical containment count; requires measured profile-specific capacity and headroom.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SISTER, MK, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
N_U = max_k ceil(E_k/((1-h_k)*C_Uk))
Statement
When typed inputs and evidence gates pass, evaluate F-027; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: count; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-027’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-027); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-027 and applicable family/product/representation white papers
Type
count
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
28.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_027 : Formula<count>
definition "Canonical pre-Pearl physical containment count; requires measured
profile-specific capacity and headroom."
↪
expression `N_U = max_k ceil(E_k/((1-h_k)*C_Uk))`
participants ["SISTER", "MK", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
58


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
28.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-027 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 59 of 105


Chapter 29
F-028 - Byte balance
Exact expression
r_B = B_alloc-B_active-B_released-B_retained-B_exported-B_compacted
Meaning. Discrete memory reconciliation requires zero residual unless transformed.
Bound manifestations. JO, M3, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_028
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MERMAID
Declaration
formula F-028 ’Byte balance’
Definition
Discrete memory reconciliation requires zero residual unless transformed.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r_B = B_alloc-B_active-B_released-B_retained-B_exported-B_compacted
Statement
When typed inputs and evidence gates pass, evaluate F-028; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: bytes; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-028’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-028); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-028 and applicable family/product/representation white papers
Type
bytes
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
29.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_028 : Formula<bytes>
definition "Discrete memory reconciliation requires zero residual unless transformed."
expression `r_B = B_alloc-B_active-B_released-B_retained-B_exported-B_compacted`
participants ["JO", "M3", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
60


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
29.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-028 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 61 of 105


Chapter 30
F-029 - Residual consequence
Exact expression
C_B = integral B_residual(t)dt
Meaning. Time-weighted residual memory consequence.
Bound manifestations. JO, M3, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.physics.balance_containment_evidence
Namespace
MJ.PBMEF.physics.balance_containment_evidence.F_029
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MERMAID
Declaration
formula F-029 ’Residual consequence’
Definition
Time-weighted residual memory consequence.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
C_B = integral B_residual(t)dt
Statement
When typed inputs and evidence gates pass, evaluate F-029; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: byte-seconds; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-029’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-029); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-029 and applicable family/product/representation white papers
Type
byte-seconds
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
30.1 Gateway life-cycle example
module MJ.PBMEF.physics.balance_containment_evidence {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_029 : Formula<byte-seconds>
definition "Time-weighted residual memory consequence."
expression `C_B = integral B_residual(t)dt`
participants ["JO", "M3", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
62


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
30.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-029 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 63 of 105


Chapter 31
F-030 - Protected liquidity
Exact expression
L_protected_H = O_near_H+R_emergency_H+R_tax_H+R_fees_H+U_cash_H
Meaning. Liquidity first.
Bound manifestations. SHIVA, MERMAID, MK, JO
Gateway stage. Mermaid/Shiva financial analysis and reconciliation before MJ decision
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_030
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-030 ’Protected liquidity’
Definition
Liquidity first.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MERMAID, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Mermaid/Shiva financial analysis and reconciliation before MJ decision
Expression
L_protected_H = O_near_H+R_emergency_H+R_tax_H+R_fees_H+U_cash_H
Statement
When typed inputs and evidence gates pass, evaluate F-030; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: currency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-030’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-030); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-030 and applicable family/product/representation white papers
Type
currency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Mermaid/Shiva financial analysis and reconciliation before MJ decision’; physical_validation=false;
authority=false
31.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_030 : Formula<currency>
definition "Liquidity first."
expression `L_protected_H = O_near_H+R_emergency_H+R_tax_H+R_fees_H+U_cash_H`
participants ["SHIVA", "MERMAID", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
64


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
31.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-030 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 65 of 105


Chapter 32
F-031 - Investable surplus
Exact expression
S_investable_L = max(0,L_available_L-L_protected_H)
Meaning. Only surplus may enter risk analysis.
Bound manifestations. SHIVA, MERMAID, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_031
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-031 ’Investable surplus’
Definition
Only surplus may enter risk analysis.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
S_investable_L = max(0,L_available_L-L_protected_H)
Statement
When typed inputs and evidence gates pass, evaluate F-031; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: currency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-031’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-031); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-031 and applicable family/product/representation white papers
Type
currency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
32.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_031 : Formula<currency>
definition "Only surplus may enter risk analysis."
expression `S_investable_L = max(0,L_available_L-L_protected_H)`
participants ["SHIVA", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
66


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
32.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-031 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 67 of 105


Chapter 33
F-032 - Risk-capital ceiling
Exact expression
A_risk_max = min(S_investable_L,L_risk,L_product,L_regulatory,L_custody,L_concentration)
Meaning. Hard minimum across constraints.
Bound manifestations. SHIVA, MERMAID, MK, MJ
Gateway stage. Mermaid/Shiva financial analysis and reconciliation before MJ decision
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_032
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.MJ
Declaration
formula F-032 ’Risk-capital ceiling’
Definition
Hard minimum across constraints.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MERMAID, MK, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Mermaid/Shiva financial analysis and reconciliation before MJ decision
Expression
A_risk_max = min(S_investable_L,L_risk,L_product,L_regulatory,L_custody,L_concentration)
Statement
When typed inputs and evidence gates pass, evaluate F-032; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: currency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-032’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-032); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-032 and applicable family/product/representation white papers
Type
currency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Mermaid/Shiva financial analysis and reconciliation before MJ decision’; physical_validation=false;
authority=false
33.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_032 : Formula<currency>
definition "Hard minimum across constraints."
expression `A_risk_max =
min(S_investable_L,L_risk,L_product,L_regulatory,L_custody,L_concentration)`
↪
participants ["SHIVA", "MERMAID", "MK", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
68


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
33.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-032 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 69 of 105


Chapter 34
F-033 - Portfolio concentration
Exact expression
C_i = abs(V_i_H)/V_portfolio_L
Meaning. Asset concentration.
Bound manifestations. SHIVA, MERMAID, JO
Gateway stage. Mermaid/Shiva financial analysis and reconciliation before MJ decision
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_033
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-033 ’Portfolio concentration’
Definition
Asset concentration.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Mermaid/Shiva financial analysis and reconciliation before MJ decision
Expression
C_i = abs(V_i_H)/V_portfolio_L
Statement
When typed inputs and evidence gates pass, evaluate F-033; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-033’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-033); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-033 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Mermaid/Shiva financial analysis and reconciliation before MJ decision’; physical_validation=false;
authority=false
34.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_033 : Formula<ratio>
definition "Asset concentration."
expression `C_i = abs(V_i_H)/V_portfolio_L`
participants ["SHIVA", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
70


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
34.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-033 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 71 of 105


Chapter 35
F-034 - Portfolio variance
Exact expression
sigma_p^2 = w^T Sigma w
Meaning. Portfolio variance with evidenced covariance.
Bound manifestations. SHIVA, MERMAID, MK
Gateway stage. Mermaid/Shiva financial analysis and reconciliation before MJ decision
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_034
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.MK
Declaration
formula F-034 ’Portfolio variance’
Definition
Portfolio variance with evidenced covariance.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MERMAID, MK
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Mermaid/Shiva financial analysis and reconciliation before MJ decision
Expression
sigma_p^2 = w^T Sigma w
Statement
When typed inputs and evidence gates pass, evaluate F-034; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: return^2; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-034’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-034); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-034 and applicable family/product/representation white papers
Type
return^2
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Mermaid/Shiva financial analysis and reconciliation before MJ decision’; physical_validation=false;
authority=false
35.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_034 : Formula<return^2>
definition "Portfolio variance with evidenced covariance."
expression `sigma_p^2 = w^T Sigma w`
participants ["SHIVA", "MERMAID", "MK"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
72


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
35.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-034 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 73 of 105


Chapter 36
F-035 - Capital friction
Exact expression
F_capital_H = fees+spread+slippage+tax+custody+compliance+latency
Meaning. Typed transactional friction.
Bound manifestations. MK, SHIVA, MERMAID
Gateway stage. Mermaid/Shiva financial analysis and reconciliation before MJ decision
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_035
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MERMAID
Declaration
formula F-035 ’Capital friction’
Definition
Typed transactional friction.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, SHIVA, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Mermaid/Shiva financial analysis and reconciliation before MJ decision
Expression
F_capital_H = fees+spread+slippage+tax+custody+compliance+latency
Statement
When typed inputs and evidence gates pass, evaluate F-035; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: currency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-035’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-035); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-035 and applicable family/product/representation white papers
Type
currency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Mermaid/Shiva financial analysis and reconciliation before MJ decision’; physical_validation=false;
authority=false
36.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_035 : Formula<currency>
definition "Typed transactional friction."
expression `F_capital_H = fees+spread+slippage+tax+custody+compliance+latency`
participants ["MK", "SHIVA", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
74


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
36.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-035 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 75 of 105


Chapter 37
F-036 - Opportunity lower bound
Exact expression
O_L = Return_L-F_capital_H-RiskPenalty_H-LiquidityPenalty_H-RegulatoryUncertainty_H
Meaning. Conservative opportunity result.
Bound manifestations. SHIVA, MK, MERMAID, MJ
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_036
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.MJ
Declaration
formula F-036 ’Opportunity lower bound’
Definition
Conservative opportunity result.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MK, MERMAID, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
O_L = Return_L-F_capital_H-RiskPenalty_H-LiquidityPenalty_H-RegulatoryUncertainty_H
Statement
When typed inputs and evidence gates pass, evaluate F-036; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: currency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-036’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-036); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-036 and applicable family/product/representation white papers
Type
currency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
37.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_036 : Formula<currency>
definition "Conservative opportunity result."
expression `O_L =
Return_L-F_capital_H-RiskPenalty_H-LiquidityPenalty_H-RegulatoryUncertainty_H`
↪
participants ["SHIVA", "MK", "MERMAID", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
76


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
37.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-036 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 77 of 105


Chapter 38
F-037 - Abundance objective
Exact expression
A = sum(alpha_i*P_i)-sum(beta_j*N_j)
Meaning. Only valid with precommitted weights and compatible scales.
Bound manifestations. SHIVA, MK, JO, MJ
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_037
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MJ
Declaration
formula F-037 ’Abundance objective’
Definition
Only valid with precommitted weights and compatible scales.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MK, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
A = sum(alpha_i*P_i)-sum(beta_j*N_j)
Statement
When typed inputs and evidence gates pass, evaluate F-037; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: declared score; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-037’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-037); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-037 and applicable family/product/representation white papers
Type
declared score
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
38.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_037 : Formula<declared score>
definition "Only valid with precommitted weights and compatible scales."
expression `A = sum(alpha_i*P_i)-sum(beta_j*N_j)`
participants ["SHIVA", "MK", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
78


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
38.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-037 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 79 of 105


Chapter 39
F-038 - SHIVAS eligible value
Exact expression
V_eligible_L=max(0,V_verified_L-L_known_H-U_valuation_H)
Meaning. Internal valuation lower bound.
Bound manifestations. SHIVA, MERMAID, JO
Gateway stage. Mermaid/Shiva financial analysis and reconciliation before MJ decision
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_038
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-038 ’SHIVAS eligible value’
Definition
Internal valuation lower bound.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Mermaid/Shiva financial analysis and reconciliation before MJ decision
Expression
V_eligible_L=max(0,V_verified_L-L_known_H-U_valuation_H)
Statement
When typed inputs and evidence gates pass, evaluate F-038; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: currency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-038’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-038); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-038 and applicable family/product/representation white papers
Type
currency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Mermaid/Shiva financial analysis and reconciliation before MJ decision’; physical_validation=false;
authority=false
39.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_038 : Formula<currency>
definition "Internal valuation lower bound."
expression `V_eligible_L=max(0,V_verified_L-L_known_H-U_valuation_H)`
participants ["SHIVA", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
80


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
39.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-038 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 81 of 105


Chapter 40
F-039 - SHIVAS ceiling
Exact expression
N_max=floor(V_eligible_L/B_unit_H)
Meaning. Only when backing, rights, classification, and evidence are known.
Bound manifestations. SHIVA, MERMAID, MJ
Gateway stage. Mermaid/Shiva financial analysis and reconciliation before MJ decision
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_039
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.MJ
Declaration
formula F-039 ’SHIVAS ceiling’
Definition
Only when backing, rights, classification, and evidence are known.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SHIVA, MERMAID, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Mermaid/Shiva financial analysis and reconciliation before MJ decision
Expression
N_max=floor(V_eligible_L/B_unit_H)
Statement
When typed inputs and evidence gates pass, evaluate F-039; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: count; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-039’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-039); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-039 and applicable family/product/representation white papers
Type
count
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Mermaid/Shiva financial analysis and reconciliation before MJ decision’; physical_validation=false;
authority=false
40.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_039 : Formula<count>
definition "Only when backing, rights, classification, and evidence are known."
expression `N_max=floor(V_eligible_L/B_unit_H)`
participants ["SHIVA", "MERMAID", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
82


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
40.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-039 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 83 of 105


Chapter 41
F-040 - MK state model
Exact expression
x[t+1]=F(x[t],u[t],theta,e[t])+w[t]; y[t]=H(x[t])+v[t]
Meaning. General physics state and observation representation.
Bound manifestations. MK, JP, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_040
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO
Declaration
formula F-040 ’MK state model’
Definition
General physics state and observation representation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JP, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
x[t+1]=F(x[t],u[t],theta,e[t])+w[t]; y[t]=H(x[t])+v[t]
Statement
When typed inputs and evidence gates pass, evaluate F-040; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed state; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-040’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-040); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-040 and applicable family/product/representation white papers
Type
typed state
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
41.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_040 : Formula<typed state>
definition "General physics state and observation representation."
expression `x[t+1]=F(x[t],u[t],theta,e[t])+w[t]; y[t]=H(x[t])+v[t]`
participants ["MK", "JP", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
84


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
41.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-040 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 85 of 105


Chapter 42
F-041 - Dimensional integrity
Exact expression
dim(LHS)=dim(RHS)
Meaning. Every physical equality must be dimensionally valid.
Bound manifestations. MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_041
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-041 ’Dimensional integrity’
Definition
Every physical equality must be dimensionally valid.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
dim(LHS)=dim(RHS)
Statement
When typed inputs and evidence gates pass, evaluate F-041; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimension equality; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-041’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-041); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-041 and applicable family/product/representation white papers
Type
dimension equality
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
42.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_041 : Formula<dimension equality>
definition "Every physical equality must be dimensionally valid."
expression `dim(LHS)=dim(RHS)`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
86


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
42.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-041 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 87 of 105


Chapter 43
F-042 - Conservation residual
Exact expression
r_q=q_in-q_out-Deltaq-q_loss
Meaning. Pass only when |r_q|<=U_q.
Bound manifestations. MK, JO, EVE, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.finance.portfolio_mk_integrity
Namespace
MJ.PBMEF.finance.portfolio_mk_integrity.F_042
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MERMAID
Declaration
formula F-042 ’Conservation residual’
Definition
Pass only when |r_q|<=U_q.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, EVE, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r_q=q_in-q_out-Deltaq-q_loss
Statement
When typed inputs and evidence gates pass, evaluate F-042; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: quantity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-042’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-042); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-042 and applicable family/product/representation white papers
Type
quantity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
43.1 Gateway life-cycle example
module MJ.PBMEF.finance.portfolio_mk_integrity {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_042 : Formula<quantity>
definition "Pass only when |r_q|<=U_q."
expression `r_q=q_in-q_out-Deltaq-q_loss`
participants ["MK", "JO", "EVE", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
88


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
43.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-042 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 89 of 105


Chapter 44
F-043 - Pearl simulation ellipsoid vol-
ume
Exact expression
V_P=(4/3)*pi*a*b*c
Meaning. Hypothetical pearl-shaped simulation geometry; no physical container or dimension claim.
Bound manifestations. MK, SISTER, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_043
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-043 ’Pearl simulation ellipsoid volume’
Definition
Hypothetical pearl-shaped simulation geometry; no physical container or dimension claim.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, SISTER, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
V_P=(4/3)*pi*a*b*c
Statement
When typed inputs and evidence gates pass, evaluate F-043; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-043’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-043); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
4, 3
Reference
pathways/FORMULA-REGISTER.json#F-043 and applicable family/product/representation white papers
Type
volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
44.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_043 : Formula<volume>
definition "Hypothetical pearl-shaped simulation geometry; no physical container or
dimension claim."
↪
expression `V_P=(4/3)*pi*a*b*c`
participants ["MK", "SISTER", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
90


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
44.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-043 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 91 of 105


Chapter 45
F-044 - Pearl simulation surface-area
approximation
Exact expression
A_P~=4*pi*((a^p*b^p+a^p*c^p+b^p*c^p)/3)^(1/p), p=1.6075
Meaning. Hypothetical simulation geometry approximation; no physical wall or surface claim.
Bound manifestations. MK, BELLE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_044
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.BELLE, MJ.PBMEF.Family.JO
Declaration
formula F-044 ’Pearl simulation surface-area approximation’
Definition
Hypothetical simulation geometry approximation; no physical wall or surface claim.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, BELLE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
A_P~=4*pi*((a^p*b^p+a^p*c^p+b^p*c^p)/3)^(1/p), p=1.6075
Statement
When typed inputs and evidence gates pass, evaluate F-044; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: area; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-044’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-044); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
4, 3, 1, 1.6075
Reference
pathways/FORMULA-REGISTER.json#F-044 and applicable family/product/representation white papers
Type
area
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
45.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_044 : Formula<area>
definition "Hypothetical simulation geometry approximation; no physical wall or surface
claim."
↪
expression `A_P~=4*pi*((a^p*b^p+a^p*c^p+b^p*c^p)/3)^(1/p), p=1.6075`
participants ["MK", "BELLE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
92


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
45.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-044 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 93 of 105


Chapter 46
F-045 - Pearl simulation exposure ratio
Exact expression
chi_P=A_P/V_P
Meaning. Simulation comparison metric only; not physical breach or exposure evidence.
Bound manifestations. MK, BELLE, EVE
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_045
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.BELLE, MJ.PBMEF.Family.EVE
Declaration
formula F-045 ’Pearl simulation exposure ratio’
Definition
Simulation comparison metric only; not physical breach or exposure evidence.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, BELLE, EVE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
chi_P=A_P/V_P
Statement
When typed inputs and evidence gates pass, evaluate F-045; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: 1/length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-045’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-045); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-045 and applicable family/product/representation white papers
Type
1/length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
46.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_045 : Formula<1/length>
definition "Simulation comparison metric only; not physical breach or exposure evidence."
expression `chi_P=A_P/V_P`
participants ["MK", "BELLE", "EVE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
94


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
46.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-045 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 95 of 105


Chapter 47
F-046 - Pearl simulation capacity slack
Exact expression
S_Pk=(1-h_Pk)*C_Pk-L_Pk
Meaning. Remaining typed simulation/information capacity after declared headroom.
Bound manifestations. SISTER, EVE, M3, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_046
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK
Declaration
formula F-046 ’Pearl simulation capacity slack’
Definition
Remaining typed simulation/information capacity after declared headroom.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SISTER, EVE, M3, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
S_Pk=(1-h_Pk)*C_Pk-L_Pk
Statement
When typed inputs and evidence gates pass, evaluate F-046; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: quantity_k; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-046’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-046); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-046 and applicable family/product/representation white papers
Type
quantity_k
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
47.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_046 : Formula<quantity_k>
definition "Remaining typed simulation/information capacity after declared headroom."
expression `S_Pk=(1-h_Pk)*C_Pk-L_Pk`
participants ["SISTER", "EVE", "M3", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
96


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
47.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-046 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 97 of 105


Chapter 48
F-047 - Pearl simulation saturation ratio
Exact expression
beta_P=max_k(L_Pk/((1-h_Pk)*C_Pk))
Meaning. Simulation saturation condition only; not physical breach resistance.
Bound manifestations. MK, ANGELS, BELLATRIX, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_047
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.BELLATRIX, MJ.PBMEF.Family.JO
Declaration
formula F-047 ’Pearl simulation saturation ratio’
Definition
Simulation saturation condition only; not physical breach resistance.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, ANGELS, BELLATRIX, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
beta_P=max_k(L_Pk/((1-h_Pk)*C_Pk))
Statement
When typed inputs and evidence gates pass, evaluate F-047; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-047’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-047); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-047 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
48.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_047 : Formula<ratio>
definition "Simulation saturation condition only; not physical breach resistance."
expression `beta_P=max_k(L_Pk/((1-h_Pk)*C_Pk))`
participants ["MK", "ANGELS", "BELLATRIX", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
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48.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-047 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 99 of 105


Chapter 49
F-048 - Pearl simulation object count
Exact expression
N_P=max_k ceil(E_k/((1-h_Pk)*C_Pk))
Meaning. Number of hypothetical simulation objects needed for declared information/resource dimen-
sions.
Bound manifestations. SISTER, EVE, M3, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_048
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK
Declaration
formula F-048 ’Pearl simulation object count’
Definition
Number of hypothetical simulation objects needed for declared information/resource dimensions.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SISTER, EVE, M3, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
N_P=max_k ceil(E_k/((1-h_Pk)*C_Pk))
Statement
When typed inputs and evidence gates pass, evaluate F-048; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: count; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-048’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-048); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-048 and applicable family/product/representation white papers
Type
count
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
49.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_048 : Formula<count>
definition "Number of hypothetical simulation objects needed for declared
information/resource dimensions."
↪
expression `N_P=max_k ceil(E_k/((1-h_Pk)*C_Pk))`
participants ["SISTER", "EVE", "M3", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
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PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
49.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-048 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 101 of 105


Chapter 50
F-049 - Pearl simulation accounting bal-
ance
Exact expression
r_Pk=q_in-q_captured-q_transferred-q_retained-q_escaped-Deltaq_stored
Meaning. Simulation/accounting conservation across retained, transferred, escaped-observation, and
stored information.
Bound manifestations. EVE, MK, JO, MERMAID
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_049
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-049 ’Pearl simulation accounting balance’
Definition
Simulation/accounting conservation across retained, transferred, escaped-observation, and stored information.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
EVE, MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
r_Pk=q_in-q_captured-q_transferred-q_retained-q_escaped-Deltaq_stored
Statement
When typed inputs and evidence gates pass, evaluate F-049; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: quantity_k; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-049’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-049); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-049 and applicable family/product/representation white papers
Type
quantity_k
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
50.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_049 : Formula<quantity_k>
definition "Simulation/accounting conservation across retained, transferred,
escaped-observation, and stored information."
↪
expression `r_Pk=q_in-q_captured-q_transferred-q_retained-q_escaped-Deltaq_stored`
participants ["EVE", "MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
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Pink Paper II - F001-F050
}
50.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-049 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 103 of 105


Chapter 51
F-050 - Pearl simulated transfer oppor-
tunity
Exact expression
T_ij,k=min([S_jk]_+,[Q_ik-Q_reserve_ik]_+,C_route_k)
Meaning. Simulated transfer opportunity bounded by declared logical capacities; no physical transfer.
Bound manifestations. SISTER, EVE, M3, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_050
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK
Declaration
formula F-050 ’Pearl simulated transfer opportunity’
Definition
Simulated transfer opportunity bounded by declared logical capacities; no physical transfer.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SISTER, EVE, M3, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
T_ij,k=min([S_jk]_+,[Q_ik-Q_reserve_ik]_+,C_route_k)
Statement
When typed inputs and evidence gates pass, evaluate F-050; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: quantity_k; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-050’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-050); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-050 and applicable family/product/representation white papers
Type
quantity_k
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
51.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_050 : Formula<quantity_k>
definition "Simulated transfer opportunity bounded by declared logical capacities; no
physical transfer."
↪
expression `T_ij,k=min([S_jk]_+,[Q_ik-Q_reserve_ik]_+,C_route_k)`
participants ["SISTER", "EVE", "M3", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
104


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
51.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-050 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 105 of 105


MJ-PBMEF Pink Paper - Volume III
Formula Gateway Bindings F-051 through F-100
Michael Bangel - Author and Architect
August 2026


Contents
1
Verification method
5
2
F-051 - Pearl simulated regeneration vector
6
2.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3
F-052 - Pearl acoustic simulation wavelength
8
3.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
3.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
4
F-053 - Pearl acoustic simulation intensity
10
4.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
4.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
5
F-054 - Pearl acoustic simulation energy
12
5.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
5.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
6
F-055 - Pearl acoustic simulation observability gate
14
6.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
6.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
7
F-056 - Pearl acoustic simulation signal-to-noise
16
7.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
7.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
8
F-057 - Pearl acoustic simulation transfer function
18
8.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
8.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
9
F-058 - Pearl acoustic simulation setpoint
20
9.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
9.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
10F-059 - Bounded Pearl acoustic simulation adjustment
22
10.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
10.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
11F-060 - Pearl simulation registry reconciliation
24
11.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
11.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
12F-061 - Bangel Sheet cell state
26
12.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
12.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
13F-062 - Affected dependency closure
28
13.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
1


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Pink Paper III - F051-F100
13.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
14F-063 - Incremental recompute cost
30
14.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
14.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
15F-064 - Concurrent edit arrival
32
15.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
15.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
16F-065 - Spreadsheet service utilization
34
16.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
16.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
17F-066 - Spreadsheet worker requirement
36
17.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
17.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
18F-067 - Recalculation latency
38
18.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
18.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
19F-068 - Spreadsheet data cost
40
19.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
19.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
20F-069 - Pearl simulation partition objective
42
20.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
20.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
21F-070 - Sheet revision root
44
21.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
21.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
22F-071 - Audit-particle completeness
46
22.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
22.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
23F-072 - Iterative recalculation stability
48
23.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
23.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
24F-073 - Revision conflict gate
50
24.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
24.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
25F-074 - Freshness age
52
25.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
25.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
26F-075 - Staleness gate
54
26.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
26.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
27F-076 - Data-performance correlation
56
27.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
27.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
28F-077 - Silo unification gate
58
28.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
28.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
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PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
29F-078 - Formula verification residual
60
29.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
29.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
30F-079 - Operational intake completeness
62
30.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
30.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
31F-080 - Spreadsheet capacity gate
64
31.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
31.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
32F-081 - First-noise rectangle height
66
32.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
32.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
33F-082 - Reference gas density
68
33.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
33.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
34F-083 - 24 mg reference volume
70
34.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
34.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
35F-084 - Rectangle depth
72
35.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
35.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
36F-085 - Cone height ratio
74
36.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
36.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
37F-086 - Cone top-width ratio
76
37.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
37.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
38F-087 - Cone area by height
78
38.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
38.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
39F-088 - Cone partial volume
80
39.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
39.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
40F-089 - Full conical-frustum volume
82
40.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
40.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
41F-090 - Pearl cone-top anchor
84
41.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
41.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
42F-091 - Observed gas mass
86
42.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
42.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
43F-092 - Gas mass-flow from height
88
43.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
43.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
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PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
44F-093 - Observed gas-height predictor
90
44.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
44.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
45F-094 - Gas net-force balance
92
45.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
45.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
46F-095 - Buoyancy force
94
46.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
46.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
47F-096 - Drag force
96
47.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
47.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
48F-097 - Flow continuity
98
48.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
48.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
49F-098 - Residual reservoir capacity
100
49.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
49.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
50F-099 - Umbrella/EVE/reservoir balance
102
50.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
50.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
51F-100 - Containment modification predicate
104
51.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
51.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Document control
Project
MJ: Physics Based Measurement Engineering Framework
Project ID
MJ-PBMEF-001
Source build
MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE
Document ID
MJ-PBMEF-PINK-PAPER-001/VOL-III
Author and architect
Michael Bangel
Status
FOUNDER_REVIEW_CANDIDATE_PENDING_FREEZE
Scope
Formula-level gateway bindings for F-051 through F-100.
Claims ceiling
This document is a private pre-Day-0 review and verification candidate. It authenticates no pri-
vate key and creates no physical validation, physical operation authority, product certification,
external regulatory authority, production deployment, financial-product launch, token issuance,
AI integration, or physical-coordinate approval. Formula pages distinguish mathematical validity,
reference implementation, simulation, measured evidence, authority, and execution.
Page 4 of 105


Chapter 1
Verification method
Each formula receives the same twenty-construct Bangel identity, a gateway-stage assignment, a life-
cycle example, and explicit evidence and ethics boundaries. The repetitive structure is intentional: it
allows formula-by-formula founder review and later automated completeness checking.
5


Chapter 2
F-051 - Pearl simulated regeneration
vector
Exact expression
G_P=[G_mass,G_energy,G_bytes,G_time,G_capital]
Meaning. Hypothetical opportunity vector; creates no physical or capital value.
Bound manifestations. EVE, MERMAID, SHIVA, MK, JO
Gateway stage. N1 prediction-first allocation, M3 routing, and G123 reconciliation
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_051
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MK
Declaration
formula F-051 ’Pearl simulated regeneration vector’
Definition
Hypothetical opportunity vector; creates no physical or capital value.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
EVE, MERMAID, SHIVA, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
N1 prediction-first allocation, M3 routing, and G123 reconciliation
Expression
G_P=[G_mass,G_energy,G_bytes,G_time,G_capital]
Statement
When typed inputs and evidence gates pass, evaluate F-051; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed vector; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-051’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-051); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-051 and applicable family/product/representation white papers
Type
typed vector
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’N1 prediction-first allocation, M3 routing, and G123 reconciliation’; physical_validation=false; author-
ity=false
2.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_051 : Formula<typed vector>
definition "Hypothetical opportunity vector; creates no physical or capital value."
expression `G_P=[G_mass,G_energy,G_bytes,G_time,G_capital]`
participants ["EVE", "MERMAID", "SHIVA", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
6


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
2.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-051 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 7 of 105


Chapter 3
F-052 - Pearl acoustic simulation wave-
length
Exact expression
lambda_ac=c_medium/f_control
Meaning. Acoustic simulation variable under declared medium assumptions; no cohesion claim.
Bound manifestations. MK, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_052
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-052 ’Pearl acoustic simulation wavelength’
Definition
Acoustic simulation variable under declared medium assumptions; no cohesion claim.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
lambda_ac=c_medium/f_control
Statement
When typed inputs and evidence gates pass, evaluate F-052; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-052’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-052); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-052 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
3.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_052 : Formula<length>
definition "Acoustic simulation variable under declared medium assumptions; no cohesion
claim."
↪
expression `lambda_ac=c_medium/f_control`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
8


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
3.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-052 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 9 of 105


Chapter 4
F-053 - Pearl acoustic simulation inten-
sity
Exact expression
I_ac=p_rms^2/(rho_medium*c_medium)
Meaning. Reference simulation intensity only; no physical actuation claim.
Bound manifestations. MK, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_053
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-053 ’Pearl acoustic simulation intensity’
Definition
Reference simulation intensity only; no physical actuation claim.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
I_ac=p_rms^2/(rho_medium*c_medium)
Statement
When typed inputs and evidence gates pass, evaluate F-053; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: power/area; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-053’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-053); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-053 and applicable family/product/representation white papers
Type
power/area
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
4.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_053 : Formula<power/area>
definition "Reference simulation intensity only; no physical actuation claim."
expression `I_ac=p_rms^2/(rho_medium*c_medium)`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
10


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
4.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-053 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 11 of 105


Chapter 5
F-054 - Pearl acoustic simulation energy
Exact expression
E_ac=integral(I_ac*A_effective)dt
Meaning. Hypothetical energy accounting for a future separately permitted experiment.
Bound manifestations. MK, EVE, MERMAID, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_054
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-054 ’Pearl acoustic simulation energy’
Definition
Hypothetical energy accounting for a future separately permitted experiment.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
E_ac=integral(I_ac*A_effective)dt
Statement
When typed inputs and evidence gates pass, evaluate F-054; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: energy; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-054’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-054); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-054 and applicable family/product/representation white papers
Type
energy
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
5.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_054 : Formula<energy>
definition "Hypothetical energy accounting for a future separately permitted experiment."
expression `E_ac=integral(I_ac*A_effective)dt`
participants ["MK", "EVE", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
12


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
5.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-054 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 13 of 105


Chapter 6
F-055 - Pearl acoustic simulation ob-
servability gate
Exact expression
f_sample>=2*gamma*f_control AND f_control in calibrated_band AND SNR_f>=SNR_min
Meaning. Simulation input must be measurable to be accounted for; observability is not actuation.
Bound manifestations. MK, JO, ANGELS
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_055
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS
Declaration
formula F-055 ’Pearl acoustic simulation observability gate’
Definition
Simulation input must be measurable to be accounted for; observability is not actuation.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
MK, JO, ANGELS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
f_sample>=2*gamma*f_control AND f_control in calibrated_band AND SNR_f>=SNR_min
Statement
When typed inputs and evidence gates pass, evaluate F-055; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-055’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-055); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-055 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
6.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_055 : Formula<logical>
definition "Simulation input must be measurable to be accounted for; observability is not
actuation."
↪
expression `f_sample>=2*gamma*f_control AND f_control in calibrated_band AND
SNR_f>=SNR_min`
↪
participants ["MK", "JO", "ANGELS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
14


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
}
6.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-055 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 15 of 105


Chapter 7
F-056 - Pearl acoustic simulation signal-
to-noise
Exact expression
SNR_f=P_signal(f)/P_noise(f)
Meaning. Simulation signal-to-noise ratio; advisory and non-authorizing.
Bound manifestations. MK, SISTER, EVE, JO
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_056
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-056 ’Pearl acoustic simulation signal-to-noise’
Definition
Simulation signal-to-noise ratio; advisory and non-authorizing.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, SISTER, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
SNR_f=P_signal(f)/P_noise(f)
Statement
When typed inputs and evidence gates pass, evaluate F-056; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-056’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-056); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-056 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
7.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_056 : Formula<ratio>
definition "Simulation signal-to-noise ratio; advisory and non-authorizing."
expression `SNR_f=P_signal(f)/P_noise(f)`
participants ["MK", "SISTER", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
16


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
7.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-056 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 17 of 105


Chapter 8
F-057 - Pearl acoustic simulation trans-
fer function
Exact expression
H_P(f)=Y_P(f)/U_P(f)
Meaning. Hypothetical or measured-later response mapping; no physical Pearl article exists.
Bound manifestations. MK, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_057
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-057 ’Pearl acoustic simulation transfer function’
Definition
Hypothetical or measured-later response mapping; no physical Pearl article exists.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
H_P(f)=Y_P(f)/U_P(f)
Statement
When typed inputs and evidence gates pass, evaluate F-057; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: output/input; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-057’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-057); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-057 and applicable family/product/representation white papers
Type
output/input
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
8.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_057 : Formula<output/input>
definition "Hypothetical or measured-later response mapping; no physical Pearl article
exists."
↪
expression `H_P(f)=Y_P(f)/U_P(f)`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
18


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
8.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-057 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 19 of 105


Chapter 9
F-058 - Pearl acoustic simulation set-
point
Exact expression
f*=argmin_{f in F_safe}(J_breach+lambda_E*E_ac+lambda_T*T_transfer)
Meaning. Simulation candidate only; no physical control setpoint.
Bound manifestations. MK, BELLE, JO, MJ
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_058
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.BELLE, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MJ
Declaration
formula F-058 ’Pearl acoustic simulation setpoint’
Definition
Simulation candidate only; no physical control setpoint.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, BELLE, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
f*=argmin_{f in F_safe}(J_breach+lambda_E*E_ac+lambda_T*T_transfer)
Statement
When typed inputs and evidence gates pass, evaluate F-058; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: frequency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-058’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-058); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-058 and applicable family/product/representation white papers
Type
frequency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
9.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_058 : Formula<frequency>
definition "Simulation candidate only; no physical control setpoint."
expression `f*=argmin_{f in F_safe}(J_breach+lambda_E*E_ac+lambda_T*T_transfer)`
participants ["MK", "BELLE", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
20


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
9.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-058 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 21 of 105


Chapter 10
F-059 - Bounded Pearl acoustic simula-
tion adjustment
Exact expression
f_next=clip((2/3)f+(1/3)f_target,f-df_max,f+df_max,f_min,f_max)
Meaning. One-third-damped simulation update only.
Bound manifestations. MK, JO, M3
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_059
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-059 ’Bounded Pearl acoustic simulation adjustment’
Definition
One-third-damped simulation update only.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
f_next=clip((2/3)f+(1/3)f_target,f-df_max,f+df_max,f_min,f_max)
Statement
When typed inputs and evidence gates pass, evaluate F-059; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: frequency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-059’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-059); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2, 3, 1
Reference
pathways/FORMULA-REGISTER.json#F-059 and applicable family/product/representation white papers
Type
frequency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
10.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_059 : Formula<frequency>
definition "One-third-damped simulation update only."
expression `f_next=clip((2/3)f+(1/3)f_target,f-df_max,f+df_max,f_min,f_max)`
participants ["MK", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
22


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
10.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-059 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 23 of 105


Chapter 11
F-060 - Pearl simulation registry recon-
ciliation
Exact expression
r_registry=N_allocated+N_received-N_transferred-N_closed-N_active
Meaning. Registry count reconciliation for simulation records, not physical containers.
Bound manifestations. MERMAID, SHIVA, M3, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_060
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.JO
Declaration
formula F-060 ’Pearl simulation registry reconciliation’
Definition
Registry count reconciliation for simulation records, not physical containers.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MERMAID, SHIVA, M3, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
r_registry=N_allocated+N_received-N_transferred-N_closed-N_active
Statement
When typed inputs and evidence gates pass, evaluate F-060; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: count; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-060’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-060); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-060 and applicable family/product/representation white papers
Type
count
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
11.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_060 : Formula<count>
definition "Registry count reconciliation for simulation records, not physical containers."
expression `r_registry=N_allocated+N_received-N_transferred-N_closed-N_active`
participants ["MERMAID", "SHIVA", "M3", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
24


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
11.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-060 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 25 of 105


Chapter 12
F-061 - Bangel Sheet cell state
Exact expression
C_ij=<value,unit,uncertainty,formula,revision,lineage,authority,evidence>
Meaning. Every cell is a governed measurement object, not an untyped mutable value.
Bound manifestations. Bangel, JP, MK, JO
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_061
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-061 ’Bangel Sheet cell state’
Definition
Every cell is a governed measurement object, not an untyped mutable value.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
Bangel, JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
C_ij=<value,unit,uncertainty,formula,revision,lineage,authority,evidence>
Statement
When typed inputs and evidence gates pass, evaluate F-061; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed object; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-061’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-061); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-061 and applicable family/product/representation white papers
Type
typed object
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
12.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_061 : Formula<typed object>
definition "Every cell is a governed measurement object, not an untyped mutable value."
expression `C_ij=<value,unit,uncertainty,formula,revision,lineage,authority,evidence>`
participants ["Bangel", "JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
26


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
12.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-061 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 27 of 105


Chapter 13
F-062 - Affected dependency closure
Exact expression
A(U)=Reachable_G(U)
Meaning. Only cells reachable from changed cells are eligible for incremental recomputation.
Bound manifestations. JP, JO, M3
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_062
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-062 ’Affected dependency closure’
Definition
Only cells reachable from changed cells are eligible for incremental recomputation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
A(U)=Reachable_G(U)
Statement
When typed inputs and evidence gates pass, evaluate F-062; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: cell set; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-062’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-062); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-062 and applicable family/product/representation white papers
Type
cell set
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
13.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_062 : Formula<cell set>
definition "Only cells reachable from changed cells are eligible for incremental
recomputation."
↪
expression `A(U)=Reachable_G(U)`
participants ["JP", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
28


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
13.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-062 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 29 of 105


Chapter 14
F-063 - Incremental recompute cost
Exact expression
C_recalc=sum_{v in A}c_v+sum_{e in E(A)}t_e
Meaning. Measured compute and transfer work for an affected dependency closure.
Bound manifestations. MK, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_063
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-063 ’Incremental recompute cost’
Definition
Measured compute and transfer work for an affected dependency closure.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
C_recalc=sum_{v in A}c_v+sum_{e in E(A)}t_e
Statement
When typed inputs and evidence gates pass, evaluate F-063; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: work units; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-063’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-063); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-063 and applicable family/product/representation white papers
Type
work units
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
14.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_063 : Formula<work units>
definition "Measured compute and transfer work for an affected dependency closure."
expression `C_recalc=sum_{v in A}c_v+sum_{e in E(A)}t_e`
participants ["MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
30


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
14.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-063 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 31 of 105


Chapter 15
F-064 - Concurrent edit arrival
Exact expression
lambda_total=N_users*lambda_user
Meaning. Aggregate update arrival rate from measured concurrent-user activity.
Bound manifestations. JO, M3, MK
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_064
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK
Declaration
formula F-064 ’Concurrent edit arrival’
Definition
Aggregate update arrival rate from measured concurrent-user activity.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JO, M3, MK
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
lambda_total=N_users*lambda_user
Statement
When typed inputs and evidence gates pass, evaluate F-064; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: operations/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-064’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-064); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-064 and applicable family/product/representation white papers
Type
operations/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
15.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_064 : Formula<operations/time>
definition "Aggregate update arrival rate from measured concurrent-user activity."
expression `lambda_total=N_users*lambda_user`
participants ["JO", "M3", "MK"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
32


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
15.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-064 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 33 of 105


Chapter 16
F-065 - Spreadsheet service utilization
Exact expression
rho=lambda_total/(W*mu_worker)
Meaning. Capacity utilization for W deterministic workers.
Bound manifestations. JO, M3, MK
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_065
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK
Declaration
formula F-065 ’Spreadsheet service utilization’
Definition
Capacity utilization for W deterministic workers.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, MK
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
rho=lambda_total/(W*mu_worker)
Statement
When typed inputs and evidence gates pass, evaluate F-065; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-065’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-065); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-065 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
16.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_065 : Formula<ratio>
definition "Capacity utilization for W deterministic workers."
expression `rho=lambda_total/(W*mu_worker)`
participants ["JO", "M3", "MK"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
34


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
16.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-065 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 35 of 105


Chapter 17
F-066 - Spreadsheet worker require-
ment
Exact expression
W_min=ceil(lambda_total/(rho_max*mu_worker))
Meaning. Minimum worker count for a precommitted utilization ceiling.
Bound manifestations. JO, M3, MJOS
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_066
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MJOS
Declaration
formula F-066 ’Spreadsheet worker requirement’
Definition
Minimum worker count for a precommitted utilization ceiling.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, MJOS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
W_min=ceil(lambda_total/(rho_max*mu_worker))
Statement
When typed inputs and evidence gates pass, evaluate F-066; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: count; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-066’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-066); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-066 and applicable family/product/representation white papers
Type
count
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
17.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_066 : Formula<count>
definition "Minimum worker count for a precommitted utilization ceiling."
expression `W_min=ceil(lambda_total/(rho_max*mu_worker))`
participants ["JO", "M3", "MJOS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
36


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
17.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-066 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 37 of 105


Chapter 18
F-067 - Recalculation latency
Exact expression
T_recalc=T_parse+T_dependency+max_p(T_partition,p)+T_commit
Meaning. End-to-end recalculation latency across logical Pearl simulation partitions.
Bound manifestations. MK, JO, M3
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_067
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-067 ’Recalculation latency’
Definition
End-to-end recalculation latency across logical Pearl simulation partitions.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
T_recalc=T_parse+T_dependency+max_p(T_partition,p)+T_commit
Statement
When typed inputs and evidence gates pass, evaluate F-067; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-067’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-067); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-067 and applicable family/product/representation white papers
Type
time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
18.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_067 : Formula<time>
definition "End-to-end recalculation latency across logical Pearl simulation partitions."
expression `T_recalc=T_parse+T_dependency+max_p(T_partition,p)+T_commit`
participants ["MK", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
38


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
18.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-067 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 39 of 105


Chapter 19
F-068 - Spreadsheet data cost
Exact expression
C_data=B_store*c_store+B_transfer*c_transfer+t_cpu*c_cpu
Meaning. Storage, transfer, and compute cost remain separately evidenced before aggregation.
Bound manifestations. MERMAID, SHIVA, MK, JO
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_068
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-068 ’Spreadsheet data cost’
Definition
Storage, transfer, and compute cost remain separately evidenced before aggregation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MERMAID, SHIVA, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
C_data=B_store*c_store+B_transfer*c_transfer+t_cpu*c_cpu
Statement
When typed inputs and evidence gates pass, evaluate F-068; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: cost unit; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-068’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-068); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-068 and applicable family/product/representation white papers
Type
cost unit
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
19.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_068 : Formula<cost unit>
definition "Storage, transfer, and compute cost remain separately evidenced before
aggregation."
↪
expression `C_data=B_store*c_store+B_transfer*c_transfer+t_cpu*c_cpu`
participants ["MERMAID", "SHIVA", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
40


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
19.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-068 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 41 of 105


Chapter 20
F-069 - Pearl simulation partition objec-
tive
Exact expression
J_partition=alpha*max_p(L_p)+beta*sum_cut(w_e)+gamma*R_breach+delta*R_stale
Meaning. Logical partition objective with precommitted weights; breach term is simulation risk, not
physical containment.
Bound manifestations. JP, MK, JO, SISTER
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_069
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-069 ’Pearl simulation partition objective’
Definition
Logical partition objective with precommitted weights; breach term is simulation risk, not physical containment.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
J_partition=alpha*max_p(L_p)+beta*sum_cut(w_e)+gamma*R_breach+delta*R_stale
Statement
When typed inputs and evidence gates pass, evaluate F-069; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: declared score; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-069’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-069); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-069 and applicable family/product/representation white papers
Type
declared score
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
20.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_069 : Formula<declared score>
definition "Logical partition objective with precommitted weights; breach term is
simulation risk, not physical containment."
↪
expression `J_partition=alpha*max_p(L_p)+beta*sum_cut(w_e)+gamma*R_breach+delta*R_stale`
participants ["JP", "MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
42


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
}
20.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-069 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 43 of 105


Chapter 21
F-070 - Sheet revision root
Exact expression
H_rev=SHA256(parent_root||canonical_deltas||policy_epoch)
Meaning. Every committed change creates immutable content-addressed lineage.
Bound manifestations. Bangel, JP, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_070
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-070 ’Sheet revision root’
Definition
Every committed change creates immutable content-addressed lineage.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
Bangel, JP, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
H_rev=SHA256(parent_root||canonical_deltas||policy_epoch)
Statement
When typed inputs and evidence gates pass, evaluate F-070; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: digest; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-070’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-070); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
56
Reference
pathways/FORMULA-REGISTER.json#F-070 and applicable family/product/representation white papers
Type
digest
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
21.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_070 : Formula<digest>
definition "Every committed change creates immutable content-addressed lineage."
expression `H_rev=SHA256(parent_root||canonical_deltas||policy_epoch)`
participants ["Bangel", "JP", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
44


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
21.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-070 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 45 of 105


Chapter 22
F-071 - Audit-particle completeness
Exact expression
AuditPass=AND(required_fields_present,receipts_valid)
Meaning. A critical spreadsheet command fails closed when its audit particle is incomplete.
Bound manifestations. JO, ANGELS, BELLATRIX, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_071
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.BELLATRIX, MJ.PBMEF.Family.MERMAID
Declaration
formula F-071 ’Audit-particle completeness’
Definition
A critical spreadsheet command fails closed when its audit particle is incomplete.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
JO, ANGELS, BELLATRIX, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
AuditPass=AND(required_fields_present,receipts_valid)
Statement
When typed inputs and evidence gates pass, evaluate F-071; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-071’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-071); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-071 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
22.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_071 : Formula<logical>
definition "A critical spreadsheet command fails closed when its audit particle is
incomplete."
↪
expression `AuditPass=AND(required_fields_present,receipts_valid)`
participants ["JO", "ANGELS", "BELLATRIX", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
46


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
22.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-071 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 47 of 105


Chapter 23
F-072 - Iterative recalculation stability
Exact expression
spectral_radius(J_F)<1
Meaning. Declared iterative formulas require an evidenced locally stable fixed-point regime.
Bound manifestations. JP, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_072
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-072 ’Iterative recalculation stability’
Definition
Declared iterative formulas require an evidenced locally stable fixed-point regime.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
spectral_radius(J_F)<1
Statement
When typed inputs and evidence gates pass, evaluate F-072; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-072’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-072); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-072 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
23.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_072 : Formula<logical>
definition "Declared iterative formulas require an evidenced locally stable fixed-point
regime."
↪
expression `spectral_radius(J_F)<1`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
48


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
23.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-072 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 49 of 105


Chapter 24
F-073 - Revision conflict gate
Exact expression
base_revision=head_revision OR valid_merge_receipt
Meaning. Stale writes cannot silently overwrite a newer revision.
Bound manifestations. Bangel, JO, ANGELS
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_073
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS
Declaration
formula F-073 ’Revision conflict gate’
Definition
Stale writes cannot silently overwrite a newer revision.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, JO, ANGELS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
base_revision=head_revision OR valid_merge_receipt
Statement
When typed inputs and evidence gates pass, evaluate F-073; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-073’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-073); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-073 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
24.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_073 : Formula<logical>
definition "Stale writes cannot silently overwrite a newer revision."
expression `base_revision=head_revision OR valid_merge_receipt`
participants ["Bangel", "JO", "ANGELS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
50


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
24.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-073 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 51 of 105


Chapter 25
F-074 - Freshness age
Exact expression
Age=now-observed_at
Meaning. Age of a source observation or derived cell.
Bound manifestations. JO, MK, SISTER
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_074
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SISTER
Declaration
formula F-074 ’Freshness age’
Definition
Age of a source observation or derived cell.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JO, MK, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
Age=now-observed_at
Statement
When typed inputs and evidence gates pass, evaluate F-074; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-074’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-074); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-074 and applicable family/product/representation white papers
Type
time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
25.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_074 : Formula<time>
definition "Age of a source observation or derived cell."
expression `Age=now-observed_at`
participants ["JO", "MK", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
52


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
25.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-074 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 53 of 105


Chapter 26
F-075 - Staleness gate
Exact expression
Age<=freshness_limit
Meaning. A cell is current only inside its declared freshness policy.
Bound manifestations. JO, ANGELS, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_075
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.MERMAID
Declaration
formula F-075 ’Staleness gate’
Definition
A cell is current only inside its declared freshness policy.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
JO, ANGELS, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
Age<=freshness_limit
Statement
When typed inputs and evidence gates pass, evaluate F-075; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-075’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-075); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-075 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
26.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_075 : Formula<logical>
definition "A cell is current only inside its declared freshness policy."
expression `Age<=freshness_limit`
participants ["JO", "ANGELS", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
54


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
26.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-075 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 55 of 105


Chapter 27
F-076 - Data-performance correlation
Exact expression
r_xy=Cov(X,Y)/(sigma_x*sigma_y)
Meaning. Descriptive correlation between data characteristics and performance; not a causal claim.
Bound manifestations. MK, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_076
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-076 ’Data-performance correlation’
Definition
Descriptive correlation between data characteristics and performance; not a causal claim.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r_xy=Cov(X,Y)/(sigma_x*sigma_y)
Statement
When typed inputs and evidence gates pass, evaluate F-076; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-076’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-076); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-076 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
27.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_076 : Formula<ratio>
definition "Descriptive correlation between data characteristics and performance; not a
causal claim."
↪
expression `r_xy=Cov(X,Y)/(sigma_x*sigma_y)`
participants ["MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
56


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
27.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-076 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 57 of 105


Chapter 28
F-077 - Silo unification gate
Exact expression
UnifiedMetric=SameMeaning AND SameUnit AND SamePeriod AND SameAuthority AND SameLineage
Meaning. Departmental sources unify only when semantic, unit, period, authority, and lineage condi-
tions agree.
Bound manifestations. ELSA, JP, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_077
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.ELSA, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-077 ’Silo unification gate’
Definition
Departmental sources unify only when semantic, unit, period, authority, and lineage conditions agree.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
ELSA, JP, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
UnifiedMetric=SameMeaning AND SameUnit AND SamePeriod AND SameAuthority AND SameLineage
Statement
When typed inputs and evidence gates pass, evaluate F-077; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-077’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-077); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-077 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
28.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_077 : Formula<logical>
definition "Departmental sources unify only when semantic, unit, period, authority, and
lineage conditions agree."
↪
expression `UnifiedMetric=SameMeaning AND SameUnit AND SamePeriod AND SameAuthority AND
SameLineage`
↪
participants ["ELSA", "JP", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
58


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28.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-077 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 59 of 105


Chapter 29
F-078 - Formula verification residual
Exact expression
r_formula=y_reported-y_recomputed
Meaning. Silent formula corruption is detected by independent deterministic recomputation.
Bound manifestations. JO, MK, ANGELS
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_078
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.ANGELS
Declaration
formula F-078 ’Formula verification residual’
Definition
Silent formula corruption is detected by independent deterministic recomputation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, MK, ANGELS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r_formula=y_reported-y_recomputed
Statement
When typed inputs and evidence gates pass, evaluate F-078; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: output unit; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-078’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-078); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-078 and applicable family/product/representation white papers
Type
output unit
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
29.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_078 : Formula<output unit>
definition "Silent formula corruption is detected by independent deterministic
recomputation."
↪
expression `r_formula=y_reported-y_recomputed`
participants ["JO", "MK", "ANGELS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
60


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Pink Paper III - F051-F100
29.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-078 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 61 of 105


Chapter 30
F-079 - Operational intake complete-
ness
Exact expression
IntakePass=process_defined AND users_known AND workload_known AND SLA_known AND authority_known
Meaning. Scaling work begins only after the process, concurrency, workload, service target, and au-
thority are explicit.
Bound manifestations. Bangel, ELSA, JP, JO, MJ
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_079
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.ELSA, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO
Declaration
formula F-079 ’Operational intake completeness’
Definition
Scaling work begins only after the process, concurrency, workload, service target, and authority are explicit.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, ELSA, JP, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
IntakePass=process_defined AND users_known AND workload_known AND SLA_known AND authority_known
Statement
When typed inputs and evidence gates pass, evaluate F-079; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-079’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-079); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-079 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
30.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_079 : Formula<logical>
definition "Scaling work begins only after the process, concurrency, workload, service
target, and authority are explicit."
↪
expression `IntakePass=process_defined AND users_known AND workload_known AND SLA_known
AND authority_known`
↪
participants ["Bangel", "ELSA", "JP", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
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Pink Paper III - F051-F100
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
30.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-079 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 63 of 105


Chapter 31
F-080 - Spreadsheet capacity gate
Exact expression
lambda_total<=rho_max*sum_p(mu_p) AND memory_required<=memory_available AND
cross_partition_edges<=cut_limit
↪
Meaning. Admission requires throughput, memory, and partition-boundary capacity to pass together.
Bound manifestations. MK, JO, M3, SISTER, MJOS
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_080
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.SISTER
Declaration
formula F-080 ’Spreadsheet capacity gate’
Definition
Admission requires throughput, memory, and partition-boundary capacity to pass together.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
MK, JO, M3, SISTER, MJOS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
lambda_total<=rho_max*sum_p(mu_p) AND memory_required<=memory_available AND cross_partition_edges<=cut_limit
Statement
When typed inputs and evidence gates pass, evaluate F-080; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-080’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-080); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-080 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
31.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_080 : Formula<logical>
definition "Admission requires throughput, memory, and partition-boundary capacity to pass
together."
↪
expression `lambda_total<=rho_max*sum_p(mu_p) AND memory_required<=memory_available AND
cross_partition_edges<=cut_limit`
↪
participants ["MK", "JO", "M3", "SISTER", "MJOS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
64


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Pink Paper III - F051-F100
31.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-080 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 65 of 105


Chapter 32
F-081 - First-noise rectangle height
Exact expression
H_R=h_noise,1
Meaning. Rectangle maximum height is the first validated noise-detection plane.
Bound manifestations. SISTER, MK, JO
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_081
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-081 ’First-noise rectangle height’
Definition
Rectangle maximum height is the first validated noise-detection plane.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
H_R=h_noise,1
Statement
When typed inputs and evidence gates pass, evaluate F-081; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-081’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-081); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-081 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
32.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_081 : Formula<length>
definition "Rectangle maximum height is the first validated noise-detection plane."
expression `H_R=h_noise,1`
participants ["SISTER", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
66


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
32.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-081 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 67 of 105


Chapter 33
F-082 - Reference gas density
Exact expression
rho_g=P*M/(Z*R*T)
Meaning. Actual gas density depends on measured pressure, temperature, molar mass, and compress-
ibility.
Bound manifestations. MK, JO, JP
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_082
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.JP
Declaration
formula F-082 ’Reference gas density’
Definition
Actual gas density depends on measured pressure, temperature, molar mass, and compressibility.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, JP
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
rho_g=P*M/(Z*R*T)
Statement
When typed inputs and evidence gates pass, evaluate F-082; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass/volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-082’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-082); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-082 and applicable family/product/representation white papers
Type
mass/volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
33.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_082 : Formula<mass/volume>
definition "Actual gas density depends on measured pressure, temperature, molar mass, and
compressibility."
↪
expression `rho_g=P*M/(Z*R*T)`
participants ["MK", "JO", "JP"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
68


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
33.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-082 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 69 of 105


Chapter 34
F-083 - 24 mg reference volume
Exact expression
V_24=m_24/rho_ref
Meaning. 24 mg defines a reference gas volume under a declared state and does not replace the 23 mg
floor.
Bound manifestations. JP, MK, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_083
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-083 ’24 mg reference volume’
Definition
24 mg defines a reference gas volume under a declared state and does not replace the 23 mg floor.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
V_24=m_24/rho_ref
Statement
When typed inputs and evidence gates pass, evaluate F-083; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-083’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-083); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
4
Reference
pathways/FORMULA-REGISTER.json#F-083 and applicable family/product/representation white papers
Type
volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
34.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_083 : Formula<volume>
definition "24 mg defines a reference gas volume under a declared state and does not
replace the 23 mg floor."
↪
expression `V_24=m_24/rho_ref`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
70


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
34.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-083 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 71 of 105


Chapter 35
F-084 - Rectangle depth
Exact expression
D_R=V_24/(W_R*H_R)
Meaning. Reference depth adapts to measured height and declared width.
Bound manifestations. SISTER, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_084
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-084 ’Rectangle depth’
Definition
Reference depth adapts to measured height and declared width.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
D_R=V_24/(W_R*H_R)
Statement
When typed inputs and evidence gates pass, evaluate F-084; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-084’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-084); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
4
Reference
pathways/FORMULA-REGISTER.json#F-084 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
35.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_084 : Formula<length>
definition "Reference depth adapts to measured height and declared width."
expression `D_R=V_24/(W_R*H_R)`
participants ["SISTER", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
72


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
35.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-084 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 73 of 105


Chapter 36
F-085 - Cone height ratio
Exact expression
H_C=k_H*H_R; k_H,std=2
Meaning. Standard cone height is twice rectangle height.
Bound manifestations. JP, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_085
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-085 ’Cone height ratio’
Definition
Standard cone height is twice rectangle height.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
H_C=k_H*H_R; k_H,std=2
Statement
When typed inputs and evidence gates pass, evaluate F-085; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-085’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-085); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-085 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
36.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_085 : Formula<length>
definition "Standard cone height is twice rectangle height."
expression `H_C=k_H*H_R; k_H,std=2`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
74


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
36.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-085 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 75 of 105


Chapter 37
F-086 - Cone top-width ratio
Exact expression
W_T=k_W*W_B; k_W,std=2
Meaning. Standard top characteristic width is twice bottom width.
Bound manifestations. JP, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_086
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-086 ’Cone top-width ratio’
Definition
Standard top characteristic width is twice bottom width.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
W_T=k_W*W_B; k_W,std=2
Statement
When typed inputs and evidence gates pass, evaluate F-086; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-086’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-086); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-086 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
37.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_086 : Formula<length>
definition "Standard top characteristic width is twice bottom width."
expression `W_T=k_W*W_B; k_W,std=2`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
76


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
37.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-086 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 77 of 105


Chapter 38
F-087 - Cone area by height
Exact expression
A(z)=A_B*(1+(k_W-1)*z/H_C)^2
Meaning. Similar-section conical expansion area.
Bound manifestations. MK, JO, SISTER
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_087
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-087 ’Cone area by height’
Definition
Similar-section conical expansion area.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
A(z)=A_B*(1+(k_W-1)*z/H_C)^2
Statement
When typed inputs and evidence gates pass, evaluate F-087; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: area; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-087’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-087); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1, 2
Reference
pathways/FORMULA-REGISTER.json#F-087 and applicable family/product/representation white papers
Type
area
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
38.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_087 : Formula<area>
definition "Similar-section conical expansion area."
expression `A(z)=A_B*(1+(k_W-1)*z/H_C)^2`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
78


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
38.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-087 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 79 of 105


Chapter 39
F-088 - Cone partial volume
Exact expression
V_C(z)=A_B*(z+(k_W-1)z^2/H_C+(k_W-1)^2*z^3/(3H_C^2))
Meaning. Volume up to observed gas height.
Bound manifestations. MK, JO, SISTER
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_088
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-088 ’Cone partial volume’
Definition
Volume up to observed gas height.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
V_C(z)=A_B*(z+(k_W-1)z^2/H_C+(k_W-1)^2*z^3/(3H_C^2))
Statement
When typed inputs and evidence gates pass, evaluate F-088; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-088’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-088); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1, 2, 3
Reference
pathways/FORMULA-REGISTER.json#F-088 and applicable family/product/representation white papers
Type
volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
39.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_088 : Formula<volume>
definition "Volume up to observed gas height."
expression `V_C(z)=A_B*(z+(k_W-1)z^2/H_C+(k_W-1)^2*z^3/(3H_C^2))`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
80


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
39.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-088 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 81 of 105


Chapter 40
F-089 - Full conical-frustum volume
Exact expression
V_C=H_C/3*(A_B+sqrt(A_B*A_T)+A_T)
Meaning. Full conical expansion volume.
Bound manifestations. MK, JO, JP
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_089
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.JP
Declaration
formula F-089 ’Full conical-frustum volume’
Definition
Full conical expansion volume.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, JP
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
V_C=H_C/3*(A_B+sqrt(A_B*A_T)+A_T)
Statement
When typed inputs and evidence gates pass, evaluate F-089; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-089’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-089); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
3
Reference
pathways/FORMULA-REGISTER.json#F-089 and applicable family/product/representation white papers
Type
volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
40.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_089 : Formula<volume>
definition "Full conical expansion volume."
expression `V_C=H_C/3*(A_B+sqrt(A_B*A_T)+A_T)`
participants ["MK", "JO", "JP"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
82


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
40.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-089 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 83 of 105


Chapter 41
F-090 - Pearl cone-top anchor
Exact expression
z_P0=H_R+H_C; standard=3H_R
Meaning. Pearl simulation begins at the top-of-cone information plane.
Bound manifestations. PEARL, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_090
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.PEARL, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-090 ’Pearl cone-top anchor’
Definition
Pearl simulation begins at the top-of-cone information plane.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
PEARL, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
z_P0=H_R+H_C; standard=3H_R
Statement
When typed inputs and evidence gates pass, evaluate F-090; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-090’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-090); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
3
Reference
pathways/FORMULA-REGISTER.json#F-090 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
41.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_090 : Formula<length>
definition "Pearl simulation begins at the top-of-cone information plane."
expression `z_P0=H_R+H_C; standard=3H_R`
participants ["PEARL", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
84


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
41.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-090 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 85 of 105


Chapter 42
F-091 - Observed gas mass
Exact expression
m_g=rho_g*V_C(h_g)
Meaning. Gas mass from observed height and state-dependent density.
Bound manifestations. MK, EVE, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_091
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-091 ’Observed gas mass’
Definition
Gas mass from observed height and state-dependent density.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
m_g=rho_g*V_C(h_g)
Statement
When typed inputs and evidence gates pass, evaluate F-091; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-091’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-091); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-091 and applicable family/product/representation white papers
Type
mass
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
42.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_091 : Formula<mass>
definition "Gas mass from observed height and state-dependent density."
expression `m_g=rho_g*V_C(h_g)`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
86


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
42.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-091 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 87 of 105


Chapter 43
F-092 - Gas mass-flow from height
Exact expression
m_dot=rho*A(h_g)*h_dot_g+V_C(h_g)*rho_dot
Meaning. Mass-flow accounting includes density changes.
Bound manifestations. MK, EVE, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_092
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-092 ’Gas mass-flow from height’
Definition
Mass-flow accounting includes density changes.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
m_dot=rho*A(h_g)*h_dot_g+V_C(h_g)*rho_dot
Statement
When typed inputs and evidence gates pass, evaluate F-092; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-092’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-092); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-092 and applicable family/product/representation white papers
Type
mass/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
43.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_092 : Formula<mass/time>
definition "Mass-flow accounting includes density changes."
expression `m_dot=rho*A(h_g)*h_dot_g+V_C(h_g)*rho_dot`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
88


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
43.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-092 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 89 of 105


Chapter 44
F-093 - Observed gas-height predictor
Exact expression
h_hat=clip(h+v*dt+0.5*a*dt^2,0,H_C)
Meaning. Bounded prediction of observed gas-front height.
Bound manifestations. SISTER, MK, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_093
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-093 ’Observed gas-height predictor’
Definition
Bounded prediction of observed gas-front height.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
h_hat=clip(h+v*dt+0.5*a*dt^2,0,H_C)
Statement
When typed inputs and evidence gates pass, evaluate F-093; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-093’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-093); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.5, 2, 0
Reference
pathways/FORMULA-REGISTER.json#F-093 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
44.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_093 : Formula<length>
definition "Bounded prediction of observed gas-front height."
expression `h_hat=clip(h+v*dt+0.5*a*dt^2,0,H_C)`
participants ["SISTER", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
90


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
44.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-093 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 91 of 105


Chapter 45
F-094 - Gas net-force balance
Exact expression
m_eff*a_z=F_b+F_p+F_act-F_d-F_wall-F_mix
Meaning. Geometry alone does not guarantee acceleration.
Bound manifestations. MK, JO, SISTER
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_094
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-094 ’Gas net-force balance’
Definition
Geometry alone does not guarantee acceleration.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
m_eff*a_z=F_b+F_p+F_act-F_d-F_wall-F_mix
Statement
When typed inputs and evidence gates pass, evaluate F-094; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: force; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-094’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-094); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-094 and applicable family/product/representation white papers
Type
force
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
45.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_094 : Formula<force>
definition "Geometry alone does not guarantee acceleration."
expression `m_eff*a_z=F_b+F_p+F_act-F_d-F_wall-F_mix`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
92


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
45.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-094 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 93 of 105


Chapter 46
F-095 - Buoyancy force
Exact expression
F_b=(rho_ambient-rho_g)*g*V_g
Meaning. Reference buoyancy term under declared environment.
Bound manifestations. MK, JO, EVE
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_095
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE
Declaration
formula F-095 ’Buoyancy force’
Definition
Reference buoyancy term under declared environment.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, EVE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
F_b=(rho_ambient-rho_g)*g*V_g
Statement
When typed inputs and evidence gates pass, evaluate F-095; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: force; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-095’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-095); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-095 and applicable family/product/representation white papers
Type
force
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
46.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_095 : Formula<force>
definition "Reference buoyancy term under declared environment."
expression `F_b=(rho_ambient-rho_g)*g*V_g`
participants ["MK", "JO", "EVE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
94


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
46.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-095 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 95 of 105


Chapter 47
F-096 - Drag force
Exact expression
F_d=0.5*C_d*rho_ambient*A_projected*u*abs(u)
Meaning. Reference drag term under declared coefficient and flow.
Bound manifestations. MK, JO, EVE
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_096
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE
Declaration
formula F-096 ’Drag force’
Definition
Reference drag term under declared coefficient and flow.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, EVE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
F_d=0.5*C_d*rho_ambient*A_projected*u*abs(u)
Statement
When typed inputs and evidence gates pass, evaluate F-096; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: force; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-096’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-096); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.5
Reference
pathways/FORMULA-REGISTER.json#F-096 and applicable family/product/representation white papers
Type
force
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
47.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_096 : Formula<force>
definition "Reference drag term under declared coefficient and flow."
expression `F_d=0.5*C_d*rho_ambient*A_projected*u*abs(u)`
participants ["MK", "JO", "EVE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
96


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
47.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-096 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 97 of 105


Chapter 48
F-097 - Flow continuity
Exact expression
Q=A(z)*u(z)
Meaning. For fixed flow, increasing area does not itself accelerate the gas.
Bound manifestations. MK, JO, SISTER
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_097
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-097 ’Flow continuity’
Definition
For fixed flow, increasing area does not itself accelerate the gas.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
Q=A(z)*u(z)
Statement
When typed inputs and evidence gates pass, evaluate F-097; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-097’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-097); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-097 and applicable family/product/representation white papers
Type
volume/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
48.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_097 : Formula<volume/time>
definition "For fixed flow, increasing area does not itself accelerate the gas."
expression `Q=A(z)*u(z)`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
98


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
48.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-097 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 99 of 105


Chapter 49
F-098 - Residual reservoir capacity
Exact expression
C_res,k=gamma_k*C_rect,k; 0<=gamma_k<1
Meaning. Residual reservoir remains smaller than rectangle reference capacity.
Bound manifestations. SISTER, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_098
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-098 ’Residual reservoir capacity’
Definition
Residual reservoir remains smaller than rectangle reference capacity.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SISTER, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
C_res,k=gamma_k*C_rect,k; 0<=gamma_k<1
Statement
When typed inputs and evidence gates pass, evaluate F-098; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed capacity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-098’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-098); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0, 1
Reference
pathways/FORMULA-REGISTER.json#F-098 and applicable family/product/representation white papers
Type
typed capacity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
49.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_098 : Formula<typed capacity>
definition "Residual reservoir remains smaller than rectangle reference capacity."
expression `C_res,k=gamma_k*C_rect,k; 0<=gamma_k<1`
participants ["SISTER", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
100


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
49.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-098 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 101 of 105


Chapter 50
F-099 - Umbrella/EVE/reservoir balance
Exact expression
q_cone=q_down+q_EVE+q_res+q_escape+r
Meaning.
Downward redistribution, EVE evidence, reservoir admission, and escape are separately
accounted.
Bound manifestations. EVE, SISTER, MERMAID
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_099
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MERMAID
Declaration
formula F-099 ’Umbrella/EVE/reservoir balance’
Definition
Downward redistribution, EVE evidence, reservoir admission, and escape are separately accounted.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
EVE, SISTER, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
q_cone=q_down+q_EVE+q_res+q_escape+r
Statement
When typed inputs and evidence gates pass, evaluate F-099; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed quantity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-099’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-099); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-099 and applicable family/product/representation white papers
Type
typed quantity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
50.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_099 : Formula<typed quantity>
definition "Downward redistribution, EVE evidence, reservoir admission, and escape are
separately accounted."
↪
expression `q_cone=q_down+q_EVE+q_res+q_escape+r`
participants ["EVE", "SISTER", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
102


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
50.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-099 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 103 of 105


Chapter 51
F-100 - Containment modification pred-
icate
Exact expression
Valid(theta)=typed&positive&recomputed&conserved&bounded&evidenced&MK&JO&MJ
Meaning. Size changes preserve core logic but require full recalculation and gates.
Bound manifestations. Bangel, JP, MK, JO, MJ
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_100
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-100 ’Containment modification predicate’
Definition
Size changes preserve core logic but require full recalculation and gates.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, JP, MK, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
Valid(theta)=typed&positive&recomputed&conserved&bounded&evidenced&MK&JO&MJ
Statement
When typed inputs and evidence gates pass, evaluate F-100; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-100’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-100); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-100 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
51.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_100 : Formula<logical>
definition "Size changes preserve core logic but require full recalculation and gates."
expression `Valid(theta)=typed&positive&recomputed&conserved&bounded&evidenced&MK&JO&MJ`
participants ["Bangel", "JP", "MK", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
104


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
51.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-100 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 105 of 105


MJ-PBMEF Pink Paper - Volume IV
Formula Gateway Bindings F-101 through F-145
Michael Bangel - Author and Architect
August 2026


Contents
1
Verification method
5
2
F-101 - Rear outlet elevation
6
2.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3
F-102 - Pearl simulation exclusion radius
8
3.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
3.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
4
F-103 - Outward-tangential outlet direction
10
4.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
4.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
5
F-104 - Outside-circle outlet path
12
5.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
5.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
6
F-105 - Reservoir volume balance
14
6.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
6.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
7
F-106 - Typed reservoir quantity balance
16
7.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
7.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
8
F-107 - Required buffer volume
18
8.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
8.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
9
F-108 - Outlet area lower bound
20
9.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
9.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
10F-109 - Circular outlet radius lower bound
22
10.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
10.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
11F-110 - Bounded drip impulse
24
11.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
11.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
12F-111 - Small-wave energy reference
26
12.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
12.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
13F-112 - Froude reference
28
13.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
1


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
13.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
14F-113 - Circular return-port area
30
14.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
14.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
15F-114 - Inward-tangential reentry components
32
15.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
15.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
16F-115 - Spiral compatibility ratio
34
16.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
16.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
17F-116 - Return continuity
36
17.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
17.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
18F-117 - Relative-frame velocity
38
18.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
18.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
19F-118 - Frictional dissipation
40
19.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
19.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
20F-119 - Recoverable friction-energy bound
42
20.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
20.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
21F-120 - Reservoir transaction gate
44
21.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
21.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
22F-121 - Re-entry swirl ratio
46
22.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
22.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
23F-122 - Re-entry processing cycle
48
23.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
23.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
24F-123 - Perspective transform residual
50
24.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
24.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
25F-124 - Physical pressure-flow dissipation
52
25.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
25.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
26F-125 - Information friction
54
26.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
26.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
27F-126 - Rotational setpoint damping
56
27.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
27.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
28F-127 - Rotational step cap
58
28.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
28.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
Page 2 of 95


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
29F-128 - Outlet transfer conservation
60
29.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
29.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
30F-129 - Re-entry recalculation vector
62
30.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
30.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
31F-130 - Re-entry admissibility predicate
64
31.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
31.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
32F-131 - Uncertainty-aware Pearl reference clearance
66
32.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
32.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
33F-132 - Outward angular-gap predicate
68
33.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
33.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
34F-133 - Available outlet pressure
70
34.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
34.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
35F-134 - Outlet pressure margin
72
35.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
35.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
36F-135 - Minimum outlet grade
74
36.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
36.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
37F-136 - Selected positive outlet grade
76
37.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
37.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
38F-137 - Incompressible reference outlet flow
78
38.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
38.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
39F-138 - Mean outlet velocity
80
39.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
39.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
40F-139 - Weber number reference
82
40.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
40.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
41F-140 - Wave amplitude ratio
84
41.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
41.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
42F-141 - Small-wave observation gate
86
42.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
42.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
43F-142 - Discrete reservoir inventory
88
43.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
43.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
Page 3 of 95


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
44F-143 - Vector reservoir headroom
90
44.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
44.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
45F-144 - Vector reservoir admission
92
45.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
45.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
46F-145 - No same-cycle feedback predicate
94
46.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
46.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
Document control
Project
MJ: Physics Based Measurement Engineering Framework
Project ID
MJ-PBMEF-001
Source build
MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE
Document ID
MJ-PBMEF-PINK-PAPER-001/VOL-IV
Author and architect
Michael Bangel
Status
FOUNDER_REVIEW_CANDIDATE_PENDING_FREEZE
Scope
Formula-level gateway bindings for F-101 through F-145.
Claims ceiling
This document is a private pre-Day-0 review and verification candidate. It authenticates no pri-
vate key and creates no physical validation, physical operation authority, product certification,
external regulatory authority, production deployment, financial-product launch, token issuance,
AI integration, or physical-coordinate approval. Formula pages distinguish mathematical validity,
reference implementation, simulation, measured evidence, authority, and execution.
Page 4 of 95


Chapter 1
Verification method
Each formula receives the same twenty-construct Bangel identity, a gateway-stage assignment, a life-
cycle example, and explicit evidence and ethics boundaries. The repetitive structure is intentional: it
allows formula-by-formula founder review and later automated completeness checking.
5


Chapter 2
F-101 - Rear outlet elevation
Exact expression
z_out=H_P-delta_z; 0<delta_z<H_P
Meaning. Outlet is below the containment maximum height.
Bound manifestations. SISTER, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_101
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-101 ’Rear outlet elevation’
Definition
Outlet is below the containment maximum height.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
z_out=H_P-delta_z; 0<delta_z<H_P
Statement
When typed inputs and evidence gates pass, evaluate F-101; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-101’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-101); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-101 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
2.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_101 : Formula<length>
definition "Outlet is below the containment maximum height."
expression `z_out=H_P-delta_z; 0<delta_z<H_P`
participants ["SISTER", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
6


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
2.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-101 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 7 of 95


Chapter 3
F-102 - Pearl simulation exclusion ra-
dius
Exact expression
R_P,sim=R_top+c_P; c_P>=0
Meaning. Nonphysical reference circle plus declared clearance.
Bound manifestations. PEARL, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_102
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.PEARL, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-102 ’Pearl simulation exclusion radius’
Definition
Nonphysical reference circle plus declared clearance.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
PEARL, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
R_P,sim=R_top+c_P; c_P>=0
Statement
When typed inputs and evidence gates pass, evaluate F-102; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-102’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-102); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-102 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
3.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_102 : Formula<length>
definition "Nonphysical reference circle plus declared clearance."
expression `R_P,sim=R_top+c_P; c_P>=0`
participants ["PEARL", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
8


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
3.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-102 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 9 of 95


Chapter 4
F-103 - Outward-tangential outlet direc-
tion
Exact expression
d_out=cos(alpha_out)t+sin(alpha_out)n_out; 0<alpha_out<pi/2
Meaning. Slight positive outward cant from the local tangent.
Bound manifestations. JP, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_103
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-103 ’Outward-tangential outlet direction’
Definition
Slight positive outward cant from the local tangent.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
d_out=cos(alpha_out)t+sin(alpha_out)n_out; 0<alpha_out<pi/2
Statement
When typed inputs and evidence gates pass, evaluate F-103; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimensionless vector; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-103’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-103); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0, 2
Reference
pathways/FORMULA-REGISTER.json#F-103 and applicable family/product/representation white papers
Type
dimensionless vector
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
4.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_103 : Formula<dimensionless vector>
definition "Slight positive outward cant from the local tangent."
expression `d_out=cos(alpha_out)t+sin(alpha_out)n_out; 0<alpha_out<pi/2`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
10


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
4.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-103 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 11 of 95


Chapter 5
F-104 - Outside-circle outlet path
Exact expression
||gamma(s)-c_P||^2=R_P^2+2R_P*s*sin(alpha_out)+s^2
Meaning. Path remains outside the Pearl simulation circle for s>0.
Bound manifestations. PEARL, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_104
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.PEARL, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-104 ’Outside-circle outlet path’
Definition
Path remains outside the Pearl simulation circle for s>0.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
PEARL, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
||gamma(s)-c_P||^2=R_P^2+2R_P*s*sin(alpha_out)+s^2
Statement
When typed inputs and evidence gates pass, evaluate F-104; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length^2; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-104’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-104); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-104 and applicable family/product/representation white papers
Type
length^2
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
5.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_104 : Formula<length^2>
definition "Path remains outside the Pearl simulation circle for s>0."
expression `||gamma(s)-c_P||^2=R_P^2+2R_P*s*sin(alpha_out)+s^2`
participants ["PEARL", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
12


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
5.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-104 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 13 of 95


Chapter 6
F-105 - Reservoir volume balance
Exact expression
dV_L/dt=Q_out-Q_return-Q_drain-Q_escape
Meaning. Connected lake-like buffer control-volume balance.
Bound manifestations. SISTER, EVE, MERMAID, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_105
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-105 ’Reservoir volume balance’
Definition
Connected lake-like buffer control-volume balance.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, EVE, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
dV_L/dt=Q_out-Q_return-Q_drain-Q_escape
Statement
When typed inputs and evidence gates pass, evaluate F-105; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-105’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-105); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-105 and applicable family/product/representation white papers
Type
volume/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
6.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_105 : Formula<volume/time>
definition "Connected lake-like buffer control-volume balance."
expression `dV_L/dt=Q_out-Q_return-Q_drain-Q_escape`
participants ["SISTER", "EVE", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
14


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
6.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-105 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 15 of 95


Chapter 7
F-106 - Typed reservoir quantity bal-
ance
Exact expression
dq_L,k/dt=q_out,k-q_return,k-q_drain,k-q_escape,k
Meaning. Per-dimension balance prevents cross-unit collapse.
Bound manifestations. SISTER, EVE, MERMAID, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_106
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-106 ’Typed reservoir quantity balance’
Definition
Per-dimension balance prevents cross-unit collapse.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, EVE, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
dq_L,k/dt=q_out,k-q_return,k-q_drain,k-q_escape,k
Statement
When typed inputs and evidence gates pass, evaluate F-106; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed quantity/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-106’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-106); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-106 and applicable family/product/representation white papers
Type
typed quantity/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
7.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_106 : Formula<typed quantity/time>
definition "Per-dimension balance prevents cross-unit collapse."
expression `dq_L,k/dt=q_out,k-q_return,k-q_drain,k-q_escape,k`
participants ["SISTER", "EVE", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
16


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
7.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-106 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 17 of 95


Chapter 8
F-107 - Required buffer volume
Exact expression
V_L,req=T_hold*max(0,Q_out,H-Q_return,L)+V_residual,H
Meaning. Conservative buffer capacity from inflow-return mismatch and residual.
Bound manifestations. MK, SISTER, JO
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_107
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.JO
Declaration
formula F-107 ’Required buffer volume’
Definition
Conservative buffer capacity from inflow-return mismatch and residual.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, SISTER, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
V_L,req=T_hold*max(0,Q_out,H-Q_return,L)+V_residual,H
Statement
When typed inputs and evidence gates pass, evaluate F-107; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-107’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-107); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-107 and applicable family/product/representation white papers
Type
volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
8.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_107 : Formula<volume>
definition "Conservative buffer capacity from inflow-return mismatch and residual."
expression `V_L,req=T_hold*max(0,Q_out,H-Q_return,L)+V_residual,H`
participants ["MK", "SISTER", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
18


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
8.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-107 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 19 of 95


Chapter 9
F-108 - Outlet area lower bound
Exact expression
A_out>=Q_design/u_out,max
Meaning. Area sizing from conservative design flow and allowable velocity.
Bound manifestations. MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_108
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-108 ’Outlet area lower bound’
Definition
Area sizing from conservative design flow and allowable velocity.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
A_out>=Q_design/u_out,max
Statement
When typed inputs and evidence gates pass, evaluate F-108; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: area; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-108’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-108); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-108 and applicable family/product/representation white papers
Type
area
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
9.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_108 : Formula<area>
definition "Area sizing from conservative design flow and allowable velocity."
expression `A_out>=Q_design/u_out,max`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
20


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
9.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-108 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 21 of 95


Chapter 10
F-109
-
Circular
outlet
radius
lower
bound
Exact expression
r_out>=sqrt(A_out/pi)
Meaning. Circular outlet radius derived from required area.
Bound manifestations. MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_109
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-109 ’Circular outlet radius lower bound’
Definition
Circular outlet radius derived from required area.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
r_out>=sqrt(A_out/pi)
Statement
When typed inputs and evidence gates pass, evaluate F-109; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-109’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-109); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-109 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
10.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_109 : Formula<length>
definition "Circular outlet radius derived from required area."
expression `r_out>=sqrt(A_out/pi)`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
22


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
10.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-109 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 23 of 95


Chapter 11
F-110 - Bounded drip impulse
Exact expression
J_drop=m_drop*v_drop<=J_drop,max
Meaning. Small-discharge reference objective; threshold requires evidence.
Bound manifestations. MK, ANGELS, JO
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_110
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.JO
Declaration
formula F-110 ’Bounded drip impulse’
Definition
Small-discharge reference objective; threshold requires evidence.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, ANGELS, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
J_drop=m_drop*v_drop<=J_drop,max
Statement
When typed inputs and evidence gates pass, evaluate F-110; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: impulse; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-110’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-110); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-110 and applicable family/product/representation white papers
Type
impulse
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
11.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_110 : Formula<impulse>
definition "Small-discharge reference objective; threshold requires evidence."
expression `J_drop=m_drop*v_drop<=J_drop,max`
participants ["MK", "ANGELS", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
24


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
11.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-110 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 25 of 95


Chapter 12
F-111 - Small-wave energy reference
Exact expression
E_wave~=0.5*rho*g*a_wave^2*A_surface
Meaning. Applies only under small-amplitude liquid-surface assumptions.
Bound manifestations. MK, JO, EVE
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_111
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE
Declaration
formula F-111 ’Small-wave energy reference’
Definition
Applies only under small-amplitude liquid-surface assumptions.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, EVE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
E_wave~=0.5*rho*g*a_wave^2*A_surface
Statement
When typed inputs and evidence gates pass, evaluate F-111; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: energy; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-111’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-111); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.5, 2
Reference
pathways/FORMULA-REGISTER.json#F-111 and applicable family/product/representation white papers
Type
energy
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
12.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_111 : Formula<energy>
definition "Applies only under small-amplitude liquid-surface assumptions."
expression `E_wave~=0.5*rho*g*a_wave^2*A_surface`
participants ["MK", "JO", "EVE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
26


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
12.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-111 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 27 of 95


Chapter 13
F-112 - Froude reference
Exact expression
Fr=U/sqrt(gL)
Meaning. Flow-regime reference; Fr<1 is a conditional subcritical target.
Bound manifestations. MK, JO
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_112
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-112 ’Froude reference’
Definition
Flow-regime reference; Fr<1 is a conditional subcritical target.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
Fr=U/sqrt(gL)
Statement
When typed inputs and evidence gates pass, evaluate F-112; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimensionless; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-112’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-112); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-112 and applicable family/product/representation white papers
Type
dimensionless
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
13.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_112 : Formula<dimensionless>
definition "Flow-regime reference; Fr<1 is a conditional subcritical target."
expression `Fr=U/sqrt(gL)`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
28


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
13.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-112 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 29 of 95


Chapter 14
F-113 - Circular return-port area
Exact expression
A_in=pi*r_in^2
Meaning. Circular re-entry cross-section.
Bound manifestations. MK, JO
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_113
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-113 ’Circular return-port area’
Definition
Circular re-entry cross-section.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
A_in=pi*r_in^2
Statement
When typed inputs and evidence gates pass, evaluate F-113; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: area; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-113’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-113); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-113 and applicable family/product/representation white papers
Type
area
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
14.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_113 : Formula<area>
definition "Circular re-entry cross-section."
expression `A_in=pi*r_in^2`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
30


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
14.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-113 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 31 of 95


Chapter 15
F-114 - Inward-tangential reentry com-
ponents
Exact expression
u_r=-U*sin(beta_in); u_theta=sigma*U*cos(beta_in)
Meaning. Small inward angle plus tangential component; no vortex proof.
Bound manifestations. SISTER, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_114
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-114 ’Inward-tangential reentry components’
Definition
Small inward angle plus tangential component; no vortex proof.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
u_r=-U*sin(beta_in); u_theta=sigma*U*cos(beta_in)
Statement
When typed inputs and evidence gates pass, evaluate F-114; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: velocity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-114’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-114); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-114 and applicable family/product/representation white papers
Type
velocity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
15.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_114 : Formula<velocity>
definition "Small inward angle plus tangential component; no vortex proof."
expression `u_r=-U*sin(beta_in); u_theta=sigma*U*cos(beta_in)`
participants ["SISTER", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
32


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
15.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-114 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 33 of 95


Chapter 16
F-115 - Spiral compatibility ratio
Exact expression
chi_spiral=|u_theta|/max(|u_r|,epsilon)
Meaning. Reference ratio for tangential-dominant reentry.
Bound manifestations. MK, JO
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_115
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-115 ’Spiral compatibility ratio’
Definition
Reference ratio for tangential-dominant reentry.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
chi_spiral=|u_theta|/max(|u_r|,epsilon)
Statement
When typed inputs and evidence gates pass, evaluate F-115; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimensionless; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-115’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-115); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-115 and applicable family/product/representation white papers
Type
dimensionless
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
16.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_115 : Formula<dimensionless>
definition "Reference ratio for tangential-dominant reentry."
expression `chi_spiral=|u_theta|/max(|u_r|,epsilon)`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
34


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
16.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-115 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 35 of 95


Chapter 17
F-116 - Return continuity
Exact expression
Q_return=A_in*u_n
Meaning. Re-entry flow through the circular port.
Bound manifestations. MK, JO, SISTER
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_116
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-116 ’Return continuity’
Definition
Re-entry flow through the circular port.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
Q_return=A_in*u_n
Statement
When typed inputs and evidence gates pass, evaluate F-116; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-116’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-116); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-116 and applicable family/product/representation white papers
Type
volume/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
17.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_116 : Formula<volume/time>
definition "Re-entry flow through the circular port."
expression `Q_return=A_in*u_n`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
36


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
17.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-116 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 37 of 95


Chapter 18
F-117 - Relative-frame velocity
Exact expression
v_rel=v_B-v_A-Omega_A x r
Meaning. Coordinate-frame-relative motion; perspective does not create energy.
Bound manifestations. MK, JO
Gateway stage. N1 prediction-first allocation, M3 routing, and G123 reconciliation
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_117
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-117 ’Relative-frame velocity’
Definition
Coordinate-frame-relative motion; perspective does not create energy.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
N1 prediction-first allocation, M3 routing, and G123 reconciliation
Expression
v_rel=v_B-v_A-Omega_A x r
Statement
When typed inputs and evidence gates pass, evaluate F-117; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: velocity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-117’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-117); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-117 and applicable family/product/representation white papers
Type
velocity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’N1 prediction-first allocation, M3 routing, and G123 reconciliation’; physical_validation=false; author-
ity=false
18.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_117 : Formula<velocity>
definition "Coordinate-frame-relative motion; perspective does not create energy."
expression `v_rel=v_B-v_A-Omega_A x r`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
38


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
18.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-117 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 39 of 95


Chapter 19
F-118 - Frictional dissipation
Exact expression
P_diss=max(0,-F_f dot v_rel)
Meaning. Measured frame-relative frictional dissipation.
Bound manifestations. MK, JO, MERMAID
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_118
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-118 ’Frictional dissipation’
Definition
Measured frame-relative frictional dissipation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
P_diss=max(0,-F_f dot v_rel)
Statement
When typed inputs and evidence gates pass, evaluate F-118; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: power; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-118’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-118); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-118 and applicable family/product/representation white papers
Type
power
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
19.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_118 : Formula<power>
definition "Measured frame-relative frictional dissipation."
expression `P_diss=max(0,-F_f dot v_rel)`
participants ["MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
40


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
19.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-118 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 41 of 95


Chapter 20
F-119
-
Recoverable
friction-energy
bound
Exact expression
E_rec<=eta_rec*integral(P_diss dt); 0<=eta_rec<=1
Meaning. No physical recovery without an evidenced conversion mechanism.
Bound manifestations. MK, JO, MERMAID, SHIVA
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_119
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.SHIVA
Declaration
formula F-119 ’Recoverable friction-energy bound’
Definition
No physical recovery without an evidenced conversion mechanism.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, MERMAID, SHIVA
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
E_rec<=eta_rec*integral(P_diss dt); 0<=eta_rec<=1
Statement
When typed inputs and evidence gates pass, evaluate F-119; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: energy; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-119’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-119); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0, 1
Reference
pathways/FORMULA-REGISTER.json#F-119 and applicable family/product/representation white papers
Type
energy
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
20.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_119 : Formula<energy>
definition "No physical recovery without an evidenced conversion mechanism."
expression `E_rec<=eta_rec*integral(P_diss dt); 0<=eta_rec<=1`
participants ["MK", "JO", "MERMAID", "SHIVA"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
42


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
20.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-119 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 43 of 95


Chapter 21
F-120 - Reservoir transaction gate
Exact expression
Admit=AngelPass&M3Lease&MKPass&JOPass&MermaidReconciled&MJPermit
Meaning. Every reservoir transfer requires safety, routing, physics, proof, reconciliation, and permit.
Bound manifestations. ANGELS, M3, MK, JO, MERMAID, MJ
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_120
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-120 ’Reservoir transaction gate’
Definition
Every reservoir transfer requires safety, routing, physics, proof, reconciliation, and permit.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
ANGELS, M3, MK, JO, MERMAID, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
Admit=AngelPass&M3Lease&MKPass&JOPass&MermaidReconciled&MJPermit
Statement
When typed inputs and evidence gates pass, evaluate F-120; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-120’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-120); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-120 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
21.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_120 : Formula<logical>
definition "Every reservoir transfer requires safety, routing, physics, proof,
reconciliation, and permit."
↪
expression `Admit=AngelPass&M3Lease&MKPass&JOPass&MermaidReconciled&MJPermit`
participants ["ANGELS", "M3", "MK", "JO", "MERMAID", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
44


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
21.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-120 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 45 of 95


Chapter 22
F-121 - Re-entry swirl ratio
Exact expression
chi_i=|u_theta|/max(|u_r|,epsilon_u)
Meaning. Represents tangential-to-inward re-entry velocity.
Bound manifestations. MK, JO
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_121
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-121 ’Re-entry swirl ratio’
Definition
Represents tangential-to-inward re-entry velocity.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
chi_i=|u_theta|/max(|u_r|,epsilon_u)
Statement
When typed inputs and evidence gates pass, evaluate F-121; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimensionless; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-121’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-121); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-121 and applicable family/product/representation white papers
Type
dimensionless
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
22.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_121 : Formula<dimensionless>
definition "Represents tangential-to-inward re-entry velocity."
expression `chi_i=|u_theta|/max(|u_r|,epsilon_u)`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
46


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
22.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-121 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 47 of 95


Chapter 23
F-122 - Re-entry processing cycle
Exact expression
cycle_reentry=cycle_exit+1
Meaning. Prohibits same-cycle feedback and creates a new receipt chain.
Bound manifestations. JO, M3, SISTER
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_122
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.SISTER
Declaration
formula F-122 ’Re-entry processing cycle’
Definition
Prohibits same-cycle feedback and creates a new receipt chain.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
cycle_reentry=cycle_exit+1
Statement
When typed inputs and evidence gates pass, evaluate F-122; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: cycle identifier; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-122’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-122); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-122 and applicable family/product/representation white papers
Type
cycle identifier
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
23.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_122 : Formula<cycle identifier>
definition "Prohibits same-cycle feedback and creates a new receipt chain."
expression `cycle_reentry=cycle_exit+1`
participants ["JO", "M3", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
48


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
23.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-122 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 49 of 95


Chapter 24
F-123 - Perspective transform residual
Exact expression
r_Pi=x_B-T_A_to_B*x_A
Meaning. Measures disagreement after transforming observations between reference frames.
Bound manifestations. MK, JO, EVE, MERMAID
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_123
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MERMAID
Declaration
formula F-123 ’Perspective transform residual’
Definition
Measures disagreement after transforming observations between reference frames.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, EVE, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
r_Pi=x_B-T_A_to_B*x_A
Statement
When typed inputs and evidence gates pass, evaluate F-123; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed vector; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-123’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-123); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-123 and applicable family/product/representation white papers
Type
typed vector
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
24.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_123 : Formula<typed vector>
definition "Measures disagreement after transforming observations between reference
frames."
↪
expression `r_Pi=x_B-T_A_to_B*x_A`
participants ["MK", "JO", "EVE", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
50


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
24.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-123 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 51 of 95


Chapter 25
F-124 - Physical pressure-flow dissipa-
tion
Exact expression
E_diss=int(Delta_p(t)*Q(t)dt)
Meaning. Stores measured physical dissipation only when pressure and flow are evidenced.
Bound manifestations. MK, JO, MERMAID
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_124
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-124 ’Physical pressure-flow dissipation’
Definition
Stores measured physical dissipation only when pressure and flow are evidenced.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
E_diss=int(Delta_p(t)*Q(t)dt)
Statement
When typed inputs and evidence gates pass, evaluate F-124; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: energy; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-124’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-124); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-124 and applicable family/product/representation white papers
Type
energy
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
25.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_124 : Formula<energy>
definition "Stores measured physical dissipation only when pressure and flow are
evidenced."
↪
expression `E_diss=int(Delta_p(t)*Q(t)dt)`
participants ["MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
52


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
25.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-124 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 53 of 95


Chapter 26
F-125 - Information friction
Exact expression
C_info=int(B_residual(t)dt)
Meaning. Stores unresolved information or memory cost without treating it as energy.
Bound manifestations. JO, M3, MERMAID
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_125
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MERMAID
Declaration
formula F-125 ’Information friction’
Definition
Stores unresolved information or memory cost without treating it as energy.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JO, M3, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
C_info=int(B_residual(t)dt)
Statement
When typed inputs and evidence gates pass, evaluate F-125; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: byte*time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-125’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-125); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-125 and applicable family/product/representation white papers
Type
byte*time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
26.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_125 : Formula<byte*time>
definition "Stores unresolved information or memory cost without treating it as energy."
expression `C_info=int(B_residual(t)dt)`
participants ["JO", "M3", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
54


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
26.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-125 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 55 of 95


Chapter 27
F-126 - Rotational setpoint damping
Exact expression
omega_tilde=(2/3)*omega+(1/3)*omega_star
Meaning. Damps the desired rotational-wave setpoint.
Bound manifestations. MK, JO, SISTER
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_126
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-126 ’Rotational setpoint damping’
Definition
Damps the desired rotational-wave setpoint.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
omega_tilde=(2/3)*omega+(1/3)*omega_star
Statement
When typed inputs and evidence gates pass, evaluate F-126; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: angular velocity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-126’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-126); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2, 3, 1
Reference
pathways/FORMULA-REGISTER.json#F-126 and applicable family/product/representation white papers
Type
angular velocity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
27.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_126 : Formula<angular velocity>
definition "Damps the desired rotational-wave setpoint."
expression `omega_tilde=(2/3)*omega+(1/3)*omega_star`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
56


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
27.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-126 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 57 of 95


Chapter 28
F-127 - Rotational step cap
Exact expression
|omega_next-omega|<=0.1*omega_scale
Meaning. Limits one-step rotational changes.
Bound manifestations. MK, JO, ANGELS
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_127
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS
Declaration
formula F-127 ’Rotational step cap’
Definition
Limits one-step rotational changes.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, ANGELS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
|omega_next-omega|<=0.1*omega_scale
Statement
When typed inputs and evidence gates pass, evaluate F-127; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: angular velocity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-127’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-127); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.1
Reference
pathways/FORMULA-REGISTER.json#F-127 and applicable family/product/representation white papers
Type
angular velocity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
28.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_127 : Formula<angular velocity>
definition "Limits one-step rotational changes."
expression `|omega_next-omega|<=0.1*omega_scale`
participants ["MK", "JO", "ANGELS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
58


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
28.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-127 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 59 of 95


Chapter 29
F-128 - Outlet transfer conservation
Exact expression
q_exit=q_lake_in+q_EVE+q_escape+r_o
Meaning. Separates lake admission, EVE observation, escape, and residual.
Bound manifestations. EVE, SISTER, MERMAID, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_128
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-128 ’Outlet transfer conservation’
Definition
Separates lake admission, EVE observation, escape, and residual.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
EVE, SISTER, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
q_exit=q_lake_in+q_EVE+q_escape+r_o
Statement
When typed inputs and evidence gates pass, evaluate F-128; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed quantity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-128’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-128); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-128 and applicable family/product/representation white papers
Type
typed quantity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
29.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_128 : Formula<typed quantity>
definition "Separates lake admission, EVE observation, escape, and residual."
expression `q_exit=q_lake_in+q_EVE+q_escape+r_o`
participants ["EVE", "SISTER", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
60


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
29.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-128 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 61 of 95


Chapter 30
F-129 - Re-entry recalculation vector
Exact expression
Delta_x=[Delta_m,Delta_W,Delta_V,Delta_rho,Delta_T,Delta_p,Delta_h]
Meaning. Declares the observed changes that trigger recalculation before re-entry.
Bound manifestations. MK, JO, EVE, SISTER
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_129
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.SISTER
Declaration
formula F-129 ’Re-entry recalculation vector’
Definition
Declares the observed changes that trigger recalculation before re-entry.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, EVE, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
Delta_x=[Delta_m,Delta_W,Delta_V,Delta_rho,Delta_T,Delta_p,Delta_h]
Statement
When typed inputs and evidence gates pass, evaluate F-129; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed vector; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-129’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-129); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-129 and applicable family/product/representation white papers
Type
typed vector
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
30.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_129 : Formula<typed vector>
definition "Declares the observed changes that trigger recalculation before re-entry."
expression `Delta_x=[Delta_m,Delta_W,Delta_V,Delta_rho,Delta_T,Delta_p,Delta_h]`
participants ["MK", "JO", "EVE", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
62


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
30.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-129 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 63 of 95


Chapter 31
F-130 - Re-entry admissibility predicate
Exact expression
Admit_re=types&units&new_cycle&capacity&wave&MK&JO&Angels&M3&MJ
Meaning. Requires complete physics, evidence, safety, routing, and authority before physical re-entry.
Bound manifestations. Bangel, JP, MK, JO, ANGELS, M3, MJ
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_130
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-130 ’Re-entry admissibility predicate’
Definition
Requires complete physics, evidence, safety, routing, and authority before physical re-entry.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, JP, MK, JO, ANGELS, M3, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
Admit_re=types&units&new_cycle&capacity&wave&MK&JO&Angels&M3&MJ
Statement
When typed inputs and evidence gates pass, evaluate F-130; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-130’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-130); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-130 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
31.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_130 : Formula<logical>
definition "Requires complete physics, evidence, safety, routing, and authority before
physical re-entry."
↪
expression `Admit_re=types&units&new_cycle&capacity&wave&MK&JO&Angels&M3&MJ`
participants ["Bangel", "JP", "MK", "JO", "ANGELS", "M3", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
64


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
31.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-130 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 65 of 95


Chapter 32
F-131 - Uncertainty-aware Pearl refer-
ence clearance
Exact expression
min_s(||gamma_out(s)-c_P||-R_P,sim) >= c_min+U_path
Meaning. Path remains outside the nonphysical Pearl simulation reference circle after uncertainty is
included.
Bound manifestations. PEARL, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_131
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.PEARL, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-131 ’Uncertainty-aware Pearl reference clearance’
Definition
Path remains outside the nonphysical Pearl simulation reference circle after uncertainty is included.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
PEARL, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
min_s(||gamma_out(s)-c_P||-R_P,sim) >= c_min+U_path
Statement
When typed inputs and evidence gates pass, evaluate F-131; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-131’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-131); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-131 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
32.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_131 : Formula<length>
definition "Path remains outside the nonphysical Pearl simulation reference circle after
uncertainty is included."
↪
expression `min_s(||gamma_out(s)-c_P||-R_P,sim) >= c_min+U_path`
participants ["PEARL", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
66


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}
32.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-131 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 67 of 95


Chapter 33
F-132 - Outward angular-gap predicate
Exact expression
abs(wrap(alpha_out-alpha_gap)) <= Delta_alpha_gap/2
Meaning. Outlet direction remains within the declared outward-facing gap.
Bound manifestations. JP, MK, JO
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_132
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-132 ’Outward angular-gap predicate’
Definition
Outlet direction remains within the declared outward-facing gap.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
abs(wrap(alpha_out-alpha_gap)) <= Delta_alpha_gap/2
Statement
When typed inputs and evidence gates pass, evaluate F-132; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-132’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-132); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-132 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
33.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_132 : Formula<logical>
definition "Outlet direction remains within the declared outward-facing gap."
expression `abs(wrap(alpha_out-alpha_gap)) <= Delta_alpha_gap/2`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
68


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
33.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-132 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 69 of 95


Chapter 34
F-133 - Available outlet pressure
Exact expression
Delta_p_available=p_containment-p_lake+rho*g*(z_out-z_lake)
Meaning. Pressure and elevation state available to drive a reference outlet flow.
Bound manifestations. MK, JO, SISTER
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_133
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-133 ’Available outlet pressure’
Definition
Pressure and elevation state available to drive a reference outlet flow.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
Delta_p_available=p_containment-p_lake+rho*g*(z_out-z_lake)
Statement
When typed inputs and evidence gates pass, evaluate F-133; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: pressure; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-133’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-133); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-133 and applicable family/product/representation white papers
Type
pressure
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
34.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_133 : Formula<pressure>
definition "Pressure and elevation state available to drive a reference outlet flow."
expression `Delta_p_available=p_containment-p_lake+rho*g*(z_out-z_lake)`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
70


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
34.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-133 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 71 of 95


Chapter 35
F-134 - Outlet pressure margin
Exact expression
Delta_p_margin=Delta_p_available-Delta_p_loss-U_Delta_p
Meaning. Conservative pressure margin after losses and uncertainty.
Bound manifestations. MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_134
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-134 ’Outlet pressure margin’
Definition
Conservative pressure margin after losses and uncertainty.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
Delta_p_margin=Delta_p_available-Delta_p_loss-U_Delta_p
Statement
When typed inputs and evidence gates pass, evaluate F-134; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: pressure; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-134’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-134); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-134 and applicable family/product/representation white papers
Type
pressure
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
35.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_134 : Formula<pressure>
definition "Conservative pressure margin after losses and uncertainty."
expression `Delta_p_margin=Delta_p_available-Delta_p_loss-U_Delta_p`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
72


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
35.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-134 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 73 of 95


Chapter 36
F-135 - Minimum outlet grade
Exact expression
alpha_min=atan(max(0,Delta_p_loss+U_Delta_p-(p_containment-p_lake))/(rho*g*L_path))
Meaning. Minimum modeled grade needed to overcome pressure deficit under declared assumptions.
Bound manifestations. JP, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_135
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-135 ’Minimum outlet grade’
Definition
Minimum modeled grade needed to overcome pressure deficit under declared assumptions.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
alpha_min=atan(max(0,Delta_p_loss+U_Delta_p-(p_containment-p_lake))/(rho*g*L_path))
Statement
When typed inputs and evidence gates pass, evaluate F-135; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: angle; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-135’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-135); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-135 and applicable family/product/representation white papers
Type
angle
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
36.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_135 : Formula<angle>
definition "Minimum modeled grade needed to overcome pressure deficit under declared
assumptions."
↪
expression
`alpha_min=atan(max(0,Delta_p_loss+U_Delta_p-(p_containment-p_lake))/(rho*g*L_path))`
↪
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
74


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
36.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-135 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 75 of 95


Chapter 37
F-136 - Selected positive outlet grade
Exact expression
alpha_selected=alpha_min+delta_alpha; delta_alpha>0
Meaning. Slight positive increase above the modeled minimum; no universal value is asserted.
Bound manifestations. JP, MK, JO, MJ
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_136
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MJ
Declaration
formula F-136 ’Selected positive outlet grade’
Definition
Slight positive increase above the modeled minimum; no universal value is asserted.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
alpha_selected=alpha_min+delta_alpha; delta_alpha>0
Statement
When typed inputs and evidence gates pass, evaluate F-136; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: angle; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-136’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-136); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0
Reference
pathways/FORMULA-REGISTER.json#F-136 and applicable family/product/representation white papers
Type
angle
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
37.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_136 : Formula<angle>
definition "Slight positive increase above the modeled minimum; no universal value is
asserted."
↪
expression `alpha_selected=alpha_min+delta_alpha; delta_alpha>0`
participants ["JP", "MK", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
76


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
37.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-136 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 77 of 95


Chapter 38
F-137 - Incompressible reference outlet
flow
Exact expression
Q_ref=C_d*A_out*sqrt(2*max(0,Delta_p_available-Delta_p_loss)/rho)
Meaning. Conditional reference flow under evidenced incompressible assumptions.
Bound manifestations. MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_137
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-137 ’Incompressible reference outlet flow’
Definition
Conditional reference flow under evidenced incompressible assumptions.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
Q_ref=C_d*A_out*sqrt(2*max(0,Delta_p_available-Delta_p_loss)/rho)
Statement
When typed inputs and evidence gates pass, evaluate F-137; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-137’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-137); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2, 0
Reference
pathways/FORMULA-REGISTER.json#F-137 and applicable family/product/representation white papers
Type
volume/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
38.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_137 : Formula<volume/time>
definition "Conditional reference flow under evidenced incompressible assumptions."
expression `Q_ref=C_d*A_out*sqrt(2*max(0,Delta_p_available-Delta_p_loss)/rho)`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
78


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
38.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-137 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 79 of 95


Chapter 39
F-138 - Mean outlet velocity
Exact expression
U_out=Q_ref/A_out
Meaning. Conditional mean velocity for the declared outlet area.
Bound manifestations. MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_138
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-138 ’Mean outlet velocity’
Definition
Conditional mean velocity for the declared outlet area.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
U_out=Q_ref/A_out
Statement
When typed inputs and evidence gates pass, evaluate F-138; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-138’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-138); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-138 and applicable family/product/representation white papers
Type
length/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
39.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_138 : Formula<length/time>
definition "Conditional mean velocity for the declared outlet area."
expression `U_out=Q_ref/A_out`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
80


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
39.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-138 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 81 of 95


Chapter 40
F-139 - Weber number reference
Exact expression
We=rho*U^2*L/sigma
Meaning. Surface-tension-to-inertia reference when the model applies.
Bound manifestations. MK, JO
Gateway stage. Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_139
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-139 ’Weber number reference’
Definition
Surface-tension-to-inertia reference when the model applies.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Reservoir/lake/re-entry reference pathway and successor-cycle evidence
Expression
We=rho*U^2*L/sigma
Statement
When typed inputs and evidence gates pass, evaluate F-139; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimensionless; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-139’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-139); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-139 and applicable family/product/representation white papers
Type
dimensionless
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Reservoir/lake/re-entry reference pathway and successor-cycle evidence’; physical_validation=false;
authority=false
40.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_139 : Formula<dimensionless>
definition "Surface-tension-to-inertia reference when the model applies."
expression `We=rho*U^2*L/sigma`
participants ["MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
82


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
40.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-139 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 83 of 95


Chapter 41
F-140 - Wave amplitude ratio
Exact expression
epsilon_a=a_wave/h_L
Meaning. Dimensionless small-amplitude observation ratio.
Bound manifestations. MK, JO, EVE
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_140
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE
Declaration
formula F-140 ’Wave amplitude ratio’
Definition
Dimensionless small-amplitude observation ratio.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, EVE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
epsilon_a=a_wave/h_L
Statement
When typed inputs and evidence gates pass, evaluate F-140; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: dimensionless; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-140’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-140); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-140 and applicable family/product/representation white papers
Type
dimensionless
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
41.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_140 : Formula<dimensionless>
definition "Dimensionless small-amplitude observation ratio."
expression `epsilon_a=a_wave/h_L`
participants ["MK", "JO", "EVE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
84


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
41.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-140 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 85 of 95


Chapter 42
F-141 - Small-wave observation gate
Exact expression
WaveGate=(Fr<=Fr_max)&(epsilon_a<=epsilon_a,max)&(We<=We_max when applicable)
Meaning. Reference gate for bounded low-amplitude observations; not proof of wave suppression.
Bound manifestations. MK, JO, ANGELS
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_141
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS
Declaration
formula F-141 ’Small-wave observation gate’
Definition
Reference gate for bounded low-amplitude observations; not proof of wave suppression.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
MK, JO, ANGELS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
WaveGate=(Fr<=Fr_max)&(epsilon_a<=epsilon_a,max)&(We<=We_max when applicable)
Statement
When typed inputs and evidence gates pass, evaluate F-141; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-141’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-141); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-141 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
42.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_141 : Formula<logical>
definition "Reference gate for bounded low-amplitude observations; not proof of wave
suppression."
↪
expression `WaveGate=(Fr<=Fr_max)&(epsilon_a<=epsilon_a,max)&(We<=We_max when applicable)`
participants ["MK", "JO", "ANGELS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
86


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
42.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-141 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 87 of 95


Chapter 43
F-142 - Discrete reservoir inventory
Exact expression
q_L,t+1=q_L,t+q_out-q_return-q_drain-q_escape-r_L
Meaning. Receipted discrete update for the separate lake/buffer control volume.
Bound manifestations. EVE, M3, MERMAID, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_142
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-142 ’Discrete reservoir inventory’
Definition
Receipted discrete update for the separate lake/buffer control volume.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
EVE, M3, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
q_L,t+1=q_L,t+q_out-q_return-q_drain-q_escape-r_L
Statement
When typed inputs and evidence gates pass, evaluate F-142; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed quantity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-142’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-142); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-142 and applicable family/product/representation white papers
Type
typed quantity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
43.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_142 : Formula<typed quantity>
definition "Receipted discrete update for the separate lake/buffer control volume."
expression `q_L,t+1=q_L,t+q_out-q_return-q_drain-q_escape-r_L`
participants ["EVE", "M3", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
88


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
43.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-142 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 89 of 95


Chapter 44
F-143 - Vector reservoir headroom
Exact expression
H_L,k=C_L,k-q_L,k
Meaning. Headroom remains separate for every resource dimension.
Bound manifestations. SISTER, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_143
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-143 ’Vector reservoir headroom’
Definition
Headroom remains separate for every resource dimension.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SISTER, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
H_L,k=C_L,k-q_L,k
Statement
When typed inputs and evidence gates pass, evaluate F-143; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed capacity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-143’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-143); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-143 and applicable family/product/representation white papers
Type
typed capacity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
44.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_143 : Formula<typed capacity>
definition "Headroom remains separate for every resource dimension."
expression `H_L,k=C_L,k-q_L,k`
participants ["SISTER", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
90


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
44.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-143 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 91 of 95


Chapter 45
F-144 - Vector reservoir admission
Exact expression
Admit_L=AND_k[q_L,k+q_in,k <= (1-h_L,k)C_L,k]
Meaning. Admission fails when any resource dimension lacks required headroom.
Bound manifestations. ANGELS, M3, MK, JO, MJ
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_144
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-144 ’Vector reservoir admission’
Definition
Admission fails when any resource dimension lacks required headroom.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
ANGELS, M3, MK, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
Admit_L=AND_k[q_L,k+q_in,k <= (1-h_L,k)C_L,k]
Statement
When typed inputs and evidence gates pass, evaluate F-144; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-144’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-144); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-144 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
45.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_144 : Formula<logical>
definition "Admission fails when any resource dimension lacks required headroom."
expression `Admit_L=AND_k[q_L,k+q_in,k <= (1-h_L,k)C_L,k]`
participants ["ANGELS", "M3", "MK", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
92


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
45.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-144 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 93 of 95


Chapter 46
F-145 - No same-cycle feedback predi-
cate
Exact expression
ReentryValid=(cycle_reentry=cycle_exit+1)&no_uncleared_generation_reuse
Meaning. Re-entry starts a new receipted cycle and cannot feed the same active generation.
Bound manifestations. M3, JO, ANGELS, MJ
Gateway stage. Mermaid/Shiva financial analysis and reconciliation before MJ decision
Construct
Formula-specific expression
Module
MJ.PBMEF.reservoir.outlet_lake_reentry_friction
Namespace
MJ.PBMEF.reservoir.outlet_lake_reentry_friction.F_145
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.MJ
Declaration
formula F-145 ’No same-cycle feedback predicate’
Definition
Re-entry starts a new receipted cycle and cannot feed the same active generation.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
M3, JO, ANGELS, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Mermaid/Shiva financial analysis and reconciliation before MJ decision
Expression
ReentryValid=(cycle_reentry=cycle_exit+1)&no_uncleared_generation_reuse
Statement
When typed inputs and evidence gates pass, evaluate F-145; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-145’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-145); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-145 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Mermaid/Shiva financial analysis and reconciliation before MJ decision’; physical_validation=false;
authority=false
46.1 Gateway life-cycle example
module MJ.PBMEF.reservoir.outlet_lake_reentry_friction {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_145 : Formula<logical>
definition "Re-entry starts a new receipted cycle and cannot feed the same active
generation."
↪
expression `ReentryValid=(cycle_reentry=cycle_exit+1)&no_uncleared_generation_reuse`
participants ["M3", "JO", "ANGELS", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
94


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper IV - F101-F145
46.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-145 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 95 of 95


MJ-PBMEF Pink Paper - Volume V
Family Manifestations and Governed Object Gateway Bindings
Michael Bangel - Author and Architect
August 2026


Contents
1
Family manifestation verification
4
2
MJ - MJ
5
2.1 Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
3
Bangel - Bangel
6
3.1 Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
4
Elsa - ELSA
7
4.1 Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
5
JP - JP
8
5.1 Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
6
Mika / MK - MK
9
6.1 Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
7
JO - JO
10
7.1 Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
8
MJOS - MJOS
11
8.1 Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
9
Angels - ANGELS
12
9.1 Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
10Bellatrix - BELLATRIX
13
10.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
11Sister - SISTER
14
11.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
12EVE - EVE
15
12.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
13Mary / M3 - M3
16
13.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
14Mermaid - MERMAID
17
14.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
15Shiva - SHIVA
18
15.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
16Shekina - SHEKINA
19
16.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
1


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper V - Family / Objects
17Belle - BELLE
20
17.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
18Lecanto - LECANTO
21
18.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
19Moana - MOANA
22
19.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
20Aviator - AVIATOR
23
20.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
21CHI - CHI
24
21.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
22WATER - WATER
25
22.1Command-life-cycle role . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
23Governed object verification
26
23.1JP_CAPO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
23.2MK_PHYSICS_CAPO
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
23.3JO_PROOF_RECEIPT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
23.4MJ_PERMIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
23.5EVE_OBSERVATION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
23.6M3_ROUTE_RECEIPT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
23.7MERMAID_ACCOUNT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
23.8SHIVA_SHELL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
23.9SHIVAS_INTERNAL_REFLECTION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
23.10CHI_VARIANCE_OBJECT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
23.11WATER_INTERVAL_STATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
23.12PASSKEY_PUBLIC_RECEIPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
23.13PEARL_VARIANCE_CONTAINER
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
23.14PEARL_ALLOCATION_RECEIPT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
23.15PEARL_ACOUSTIC_PROFILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
23.16PEARL_SYMPOSIUM_REGISTRY
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
23.17Bangel_SHEET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
23.18Bangel_SHEET_CELL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
23.19Bangel_SHEET_REVISION
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
23.20Bangel_SHEET_AUDIT_PARTICLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
23.21JPOSMJ_PRODUCT_ENVELOPE
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
23.22SISTER_PHYSICAL_CONTAINMENT_PROFILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
23.23STANDARD_CONTAINMENT_GEOMETRY_PROFILE
. . . . . . . . . . . . . . . . . . . . . . . . . . .
38
23.24REFERENCE_GAS_PROFILE_H2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
23.25CONTAINMENT_MODIFICATION_RECEIPT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
23.26CONE_TOP_PEARL_ANCHOR
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
23.27GAS_HEIGHT_OBSERVATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
23.28RESERVOIR_RETURN_LOOP_PROFILE
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
23.29OUTWARD_GAP_PATH_RECEIPT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
23.30RESERVOIR_BUFFER_ACCOUNT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
23.31CIRCULAR_REENTRY_RECEIPT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
23.32RELATIVE_FRAME_FRICTION_LEDGER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
23.33RESERVOIR_LAKE_BUFFER
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
23.34BACKSIDE_OUTLET_PORT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
23.35OUTWARD_GAP_ARC
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
23.36PEARL_REFERENCE_CIRCLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
23.37CIRCULAR_REENTRY_PORT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
23.38RESERVOIR_TRANSFER_RECEIPT
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
23.39PERSPECTIVE_FRICTION_RECEIPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
Page 2 of 46


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper V - Family / Objects
Document control
Project
MJ: Physics Based Measurement Engineering Framework
Project ID
MJ-PBMEF-001
Source build
MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE
Document ID
MJ-PBMEF-PINK-PAPER-001/VOL-V
Author and architect
Michael Bangel
Status
FOUNDER_REVIEW_CANDIDATE_PENDING_FREEZE
Scope
All family manifestations and governed objects in gateway and life-
cycle context.
Claims ceiling
This document is a private pre-Day-0 review and verification candidate. It authenticates no pri-
vate key and creates no physical validation, physical operation authority, product certification,
external regulatory authority, production deployment, financial-product launch, token issuance,
AI integration, or physical-coordinate approval. Formula pages distinguish mathematical validity,
reference implementation, simulation, measured evidence, authority, and execution.
Page 3 of 46


Chapter 1
Family manifestation verification
4


Chapter 2
MJ - MJ
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.MJ
Namespace
MJ.PBMEF.Family.MJ.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant MJ
Definition
Project root, founder-governed authority and final bounded permit decision.
Capability
bounded permit, hold, deny, project state
Participant
MJ
Relationship
Incoming: MICHAEL_BANGEL; outgoing: Bangel
Function
Project root, founder-governed authority and final bounded permit decision.
Expression
Applicable formula set and bounded family receipt
Statement
MJ contributes its role but cannot substitute for another participant.
Measurement
founder purpose, verified evidence, family receipts, Pearl and Bangel Spreadsheets decision packets
Constraint
Cannot convert unknown evidence into permission or claim external authority.
Annotation
@family(id=’MJ’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant MJ { input; verify; output; boundary; }
Literal
truth, measurement, human authority, stewardship, non-weaponization
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
ROOT
Attribute
full_family_identity=true; self_authority=false
2.1 Command-life-cycle role
At R0/R1, MJ receives only the typed inputs applicable to its role. Before N1 it may contribute semantic,
canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route, rec-
oncile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
Cannot convert unknown evidence into permission or claim external authority.
5


Chapter 3
Bangel - Bangel
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.Bangel
Namespace
MJ.PBMEF.Family.Bangel.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant Bangel
Definition
Human-facing governed language that preserves purpose and command structure.
Capability
typed command envelope, source representation, Bangel Sheet source, if/how/then operational intake
Participant
Bangel
Relationship
Incoming: MJ; outgoing: ELSA
Function
Human-facing governed language that preserves purpose and command structure.
Expression
Applicable formula set and bounded family receipt
Statement
Bangel contributes its role but cannot substitute for another participant.
Measurement
human purpose, declared scope
Constraint
No independent execution, financial issuance, or physical truth.
Annotation
@family(id=’Bangel’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant Bangel { input; verify; output; boundary; }
Literal
intent integrity, explicit types, traceability
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
3.1 Command-life-cycle role
At R0/R1, Bangel receives only the typed inputs applicable to its role.
Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No independent execution, financial issuance, or physical truth.
6


Chapter 4
Elsa - ELSA
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.ELSA
Namespace
MJ.PBMEF.Family.ELSA.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant ELSA
Definition
Deterministic semantic recovery and purpose-preservation layer.
Capability
semantic envelope, ambiguity hold
Participant
Elsa
Relationship
Incoming: Bangel; outgoing: JP
Function
Deterministic semantic recovery and purpose-preservation layer.
Expression
Applicable formula set and bounded family receipt
Statement
Elsa contributes its role but cannot substitute for another participant.
Measurement
Bangel source, context evidence
Constraint
No execution, permit, finance, or invented intent.
Annotation
@family(id=’ELSA’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant ELSA { input; verify; output; boundary; }
Literal
meaning fidelity, purpose confinement, clarity
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
4.1 Command-life-cycle role
At R0/R1, Elsa receives only the typed inputs applicable to its role. Before N1 it may contribute seman-
tic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route,
reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
No execution, permit, finance, or invented intent.
7


Chapter 5
JP - JP
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.JP
Namespace
MJ.PBMEF.Family.JP.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant JP
Definition
Canonical mathematical, algorithmic, topology, CAPO, and architecture representation.
Capability
math CAPO, algorithm CAPO, architecture CAPO, Pearl CAPO, Bangel Sheet dependency CAPO, JPOSMJ product envelope
Participant
JP
Relationship
Incoming: ELSA; outgoing: MK
Function
Canonical mathematical, algorithmic, topology, CAPO, and architecture representation.
Expression
Applicable formula set and bounded family receipt
Statement
JP contributes its role but cannot substitute for another participant.
Measurement
semantic envelope, founder laws
Constraint
Representation is not admission, execution, or authority.
Annotation
@family(id=’JP’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant JP { input; verify; output; boundary; }
Literal
mathematical rigor, provenance, equivalence
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
5.1 Command-life-cycle role
At R0/R1, JP receives only the typed inputs applicable to its role. Before N1 it may contribute semantic,
canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route, rec-
oncile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
Representation is not admission, execution, or authority.
8


Chapter 6
Mika / MK - MK
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.MK
Namespace
MJ.PBMEF.Family.MK.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant MK
Definition
Physics Modulator System for dimensional, conservation, boundary, scale, and evidence representation.
Capability
physics CAPO, not-applicable receipt, hold, technical fail, Pearl physics receipt, spreadsheet resource-physics receipt
Participant
Mika / MK
Relationship
Incoming: JP; outgoing: JO, BELLE
Function
Physics Modulator System for dimensional, conservation, boundary, scale, and evidence representation.
Expression
Applicable formula set and bounded family receipt
Statement
Mika / MK contributes its role but cannot substitute for another participant.
Measurement
JP math CAPO, environment, control volume, evidence, Pearl simulation geometry/acoustic profile, Bangel Sheet workload and dependency field
Constraint
No MJ permit, coordinate approval, physical validation, or evidence invention.
Annotation
@family(id=’MK’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant MK { input; verify; output; boundary; }
Literal
physical truth, unit integrity, conservation, uncertainty honesty
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
6.1 Command-life-cycle role
At R0/R1, Mika / MK receives only the typed inputs applicable to its role. Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No MJ permit, coordinate approval, physical validation, or evidence invention.
9


Chapter 7
JO - JO
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.JO
Namespace
MJ.PBMEF.Family.JO.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant JO
Definition
Deterministic type, unit, proof, validation, runtime, and evidence engine.
Capability
proof receipt, runtime result, hold, deny, sheet revision receipt, Pearl balance receipt
Participant
JO
Relationship
Incoming: MK; outgoing: ANGELS, BELLATRIX, SISTER, EVE
Function
Deterministic type, unit, proof, validation, runtime, and evidence engine.
Expression
Applicable formula set and bounded family receipt
Statement
JO contributes its role but cannot substitute for another participant.
Measurement
typed CAPOs, authority receipts, evidence, Bangel Sheet revisions, Pearl lifecycle packets
Constraint
No invented purpose, physics, authority, finance, or external effect.
Annotation
@family(id=’JO’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant JO { input; verify; output; boundary; }
Literal
fail closed, reproducibility, auditability
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
7.1 Command-life-cycle role
At R0/R1, JO receives only the typed inputs applicable to its role. Before N1 it may contribute semantic,
canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route, rec-
oncile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
No invented purpose, physics, authority, finance, or external effect.
10


Chapter 8
MJOS - MJOS
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.MJOS
Namespace
MJ.PBMEF.Family.MJOS.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant MJOS
Definition
Operating-system and infrastructure substrate inside MJ.
Capability
resource service, infrastructure evidence
Participant
MJOS
Relationship
Incoming: JO_EXECUTION; outgoing: receipt to MJ/JO
Function
Operating-system and infrastructure substrate inside MJ.
Expression
Applicable formula set and bounded family receipt
Statement
MJOS contributes its role but cannot substitute for another participant.
Measurement
MJ leases, JO execution plan
Constraint
Not a second authority principal.
Annotation
@family(id=’MJOS’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant MJOS { input; verify; output; boundary; }
Literal
bounded resources, continuity, isolation
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
8.1 Command-life-cycle role
At R0/R1, MJOS receives only the typed inputs applicable to its role. Before N1 it may contribute se-
mantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route,
reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
Not a second authority principal.
11


Chapter 9
Angels - ANGELS
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.ANGELS
Namespace
MJ.PBMEF.Family.ANGELS.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant ANGELS
Definition
Domain-specific observation, telemetry, hold, denial, and corrective-command family.
Capability
safety receipt, hold, deny, correction request
Participant
Angels
Relationship
Incoming: JO; outgoing: M3
Function
Domain-specific observation, telemetry, hold, denial, and corrective-command family.
Expression
Applicable formula set and bounded family receipt
Statement
Angels contributes its role but cannot substitute for another participant.
Measurement
commands, evidence, state
Constraint
No self-admission, ordinary execution, or scope expansion.
Annotation
@family(id=’ANGELS’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant ANGELS { input; verify; output; boundary; }
Literal
safety, watchfulness, correction
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION_FAMILY
Attribute
full_family_identity=true; self_authority=false
9.1 Command-life-cycle role
At R0/R1, Angels receives only the typed inputs applicable to its role.
Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No self-admission, ordinary execution, or scope expansion.
12


Chapter 10
Bellatrix - BELLATRIX
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.BELLATRIX
Namespace
MJ.PBMEF.Family.BELLATRIX.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant BELLATRIX
Definition
Independent defense, challenge, quarantine, hostile-deviation analysis, and denial.
Capability
deny, quarantine, challenge receipt
Participant
Bellatrix
Relationship
Incoming: JO; outgoing: M3
Function
Independent defense, challenge, quarantine, hostile-deviation analysis, and denial.
Expression
Applicable formula set and bounded family receipt
Statement
Bellatrix contributes its role but cannot substitute for another participant.
Measurement
commands, threat evidence
Constraint
No positive general admission.
Annotation
@family(id=’BELLATRIX’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant BELLATRIX { input; verify; output; boundary; }
Literal
defense, independence, containment
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
10.1 Command-life-cycle role
At R0/R1, Bellatrix receives only the typed inputs applicable to its role. Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No positive general admission.
13


Chapter 11
Sister - SISTER
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.SISTER
Namespace
MJ.PBMEF.Family.SISTER.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant SISTER
Definition
Predictive digital twin, preallocation evidence, anomaly detection, umbrella collection, and canonical physical containment request.
Capability
forecast, containment request, digital-twin receipt, physical containment request and Pearl simulation request
Participant
Sister
Relationship
Incoming: JO; outgoing: M3
Function
Predictive digital twin, preallocation evidence, anomaly detection, umbrella collection, and canonical physical containment request.
Expression
Applicable formula set and bounded family receipt
Statement
Sister contributes its role but cannot substitute for another participant.
Measurement
state stream, request trend, variance
Constraint
Prediction is not permission.
Annotation
@family(id=’SISTER’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant SISTER { input; verify; output; boundary; }
Literal
prediction, redundancy, early warning
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
11.1 Command-life-cycle role
At R0/R1, Sister receives only the typed inputs applicable to its role. Before N1 it may contribute se-
mantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route,
reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
Prediction is not permission.
14


Chapter 12
EVE - EVE
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.EVE
Namespace
MJ.PBMEF.Family.EVE.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant EVE
Definition
Variance, evaporative effect, screen capture, leakage, smoke-like egress, and boundary-accounting evidence.
Capability
EVE observation, capture/egress ledger, hold, Pearl escape/capture observation
Participant
EVE
Relationship
Incoming: JO; outgoing: M3
Function
Variance, evaporative effect, screen capture, leakage, smoke-like egress, and boundary-accounting evidence.
Expression
Applicable formula set and bounded family receipt
Statement
EVE contributes its role but cannot substitute for another participant.
Measurement
mass/weight states, flows, screen measurements, residuals
Constraint
No release, pricing, minting, or execution.
Annotation
@family(id=’EVE’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant EVE { input; verify; output; boundary; }
Literal
diligence, respect, loss accounting, boundary truth
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
12.1 Command-life-cycle role
At R0/R1, EVE receives only the typed inputs applicable to its role. Before N1 it may contribute seman-
tic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route,
reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
No release, pricing, minting, or execution.
15


Chapter 13
Mary / M3 - M3
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.M3
Namespace
MJ.PBMEF.Family.M3.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant M3
Definition
Bounded routing, API gateway, load balancing, connection pooling, and allocation stewardship.
Capability
route receipt, allocation lease use, return receipt, Pearl allocation/transfer receipt, Bangel Sheet partition route receipt
Participant
Mary / M3
Relationship
Incoming: ANGELS, BELLATRIX, SISTER, EVE; outgoing: MERMAID, SHIVA
Function
Bounded routing, API gateway, load balancing, connection pooling, and allocation stewardship.
Expression
Applicable formula set and bounded family receipt
Statement
Mary / M3 contributes its role but cannot substitute for another participant.
Measurement
admitted command, MJ lease, capacity evidence
Constraint
No authority minting, lease widening, or denial bypass.
Annotation
@family(id=’M3’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant M3 { input; verify; output; boundary; }
Literal
fair allocation, resource hygiene, bounded routing
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
13.1 Command-life-cycle role
At R0/R1, Mary / M3 receives only the typed inputs applicable to its role. Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No authority minting, lease widening, or denial bypass.
16


Chapter 14
Mermaid - MERMAID
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.MERMAID
Namespace
MJ.PBMEF.Family.MERMAID.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant MERMAID
Definition
Accounting, reconciliation, exposure, custody evidence, statements, tax lots, and financial consequence.
Capability
account, balance, exposure, reconciliation receipt
Participant
Mermaid
Relationship
Incoming: M3; outgoing: MJ_DECISION
Function
Accounting, reconciliation, exposure, custody evidence, statements, tax lots, and financial consequence.
Expression
Applicable formula set and bounded family receipt
Statement
Mermaid contributes its role but cannot substitute for another participant.
Measurement
transaction evidence, EVE evidence, Shiva proposal, Pearl lifecycle and Bangel Sheet audit particles
Constraint
No source-truth invention, minting, or final permit.
Annotation
@family(id=’MERMAID’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant MERMAID { input; verify; output; boundary; }
Literal
ledger truth, reconciliation, transparency
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
14.1 Command-life-cycle role
At R0/R1, Mermaid receives only the typed inputs applicable to its role. Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No source-truth invention, minting, or final permit.
17


Chapter 15
Shiva - SHIVA
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.SHIVA
Namespace
MJ.PBMEF.Family.SHIVA.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant SHIVA
Definition
Finance, money, treasury, liquidity, capital-job classification, risk/opportunity analysis, and distribution proposal.
Capability
capital proposal, job-of-money classification, distribution plan
Participant
Shiva
Relationship
Incoming: M3; outgoing: MJ_DECISION
Function
Finance, money, treasury, liquidity, capital-job classification, risk/opportunity analysis, and distribution proposal.
Expression
Applicable formula set and bounded family receipt
Statement
Shiva contributes its role but cannot substitute for another participant.
Measurement
capital purpose, Mermaid account, MK friction, risk evidence, Pearl regeneration opportunity vectors
Constraint
No banking, investment advice, custody, exchange, minting, or external operation authority.
Annotation
@family(id=’SHIVA’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant SHIVA { input; verify; output; boundary; }
Literal
liquidity first, stability, abundance with discipline, auditability
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
15.1 Command-life-cycle role
At R0/R1, Shiva receives only the typed inputs applicable to its role. Before N1 it may contribute se-
mantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route,
reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
No banking, investment advice, custody, exchange, minting, or external operation authority.
18


Chapter 16
Shekina - SHEKINA
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.SHEKINA
Namespace
MJ.PBMEF.Family.SHEKINA.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant SHEKINA
Definition
Distributed placement, replication, continuity, and infrastructure evidence.
Capability
placement receipt, continuity evidence
Participant
Shekina
Relationship
Incoming: JO_EXECUTION; outgoing: receipt to MJ/JO
Function
Distributed placement, replication, continuity, and infrastructure evidence.
Expression
Applicable formula set and bounded family receipt
Statement
Shekina contributes its role but cannot substitute for another participant.
Measurement
placement request, MJ lease
Constraint
No authority from location and no scope widening.
Annotation
@family(id=’SHEKINA’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant SHEKINA { input; verify; output; boundary; }
Literal
continuity, bounded placement, resilience
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
16.1 Command-life-cycle role
At R0/R1, Shekina receives only the typed inputs applicable to its role. Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No authority from location and no scope widening.
19


Chapter 17
Belle - BELLE
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.BELLE
Namespace
MJ.PBMEF.Family.BELLE.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant BELLE
Definition
Engineering analysis, feasibility, topology review, and bounded proposals.
Capability
engineering proposal, risk note
Participant
Belle
Relationship
Incoming: MK; outgoing: receipt to MJ/JO
Function
Engineering analysis, feasibility, topology review, and bounded proposals.
Expression
Applicable formula set and bounded family receipt
Statement
Belle contributes its role but cannot substitute for another participant.
Measurement
design CAPO, physics CAPO
Constraint
Proposal is not execution or permit.
Annotation
@family(id=’BELLE’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant BELLE { input; verify; output; boundary; }
Literal
engineering clarity, feasibility, benchmarking
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
17.1 Command-life-cycle role
At R0/R1, Belle receives only the typed inputs applicable to its role. Before N1 it may contribute se-
mantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route,
reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
Proposal is not execution or permit.
20


Chapter 18
Lecanto - LECANTO
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.LECANTO
Namespace
MJ.PBMEF.Family.LECANTO.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant LECANTO
Definition
Truthful governed visualization of state, provenance, uncertainty, and system structure.
Capability
visual representation
Participant
Lecanto
Relationship
Incoming: JO_EXECUTION; outgoing: MOANA
Function
Truthful governed visualization of state, provenance, uncertainty, and system structure.
Expression
Applicable formula set and bounded family receipt
Statement
Lecanto contributes its role but cannot substitute for another participant.
Measurement
JO evidence, Mermaid account, MK physics receipt, Bangel Sheet lineage and Pearl state
Constraint
Cannot manufacture certainty or underlying effects.
Annotation
@family(id=’LECANTO’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant LECANTO { input; verify; output; boundary; }
Literal
visibility, truth, uncertainty disclosure
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
18.1 Command-life-cycle role
At R0/R1, Lecanto receives only the typed inputs applicable to its role. Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
Cannot manufacture certainty or underlying effects.
21


Chapter 19
Moana - MOANA
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.MOANA
Namespace
MJ.PBMEF.Family.MOANA.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant MOANA
Definition
Browser and interaction presentation of governed applications and evidence.
Capability
interaction surface
Participant
Moana
Relationship
Incoming: LECANTO; outgoing: receipt to MJ/JO
Function
Browser and interaction presentation of governed applications and evidence.
Expression
Applicable formula set and bounded family receipt
Statement
Moana contributes its role but cannot substitute for another participant.
Measurement
Lecanto views, JO evidence
Constraint
No underlying effect or credential authority.
Annotation
@family(id=’MOANA’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant MOANA { input; verify; output; boundary; }
Literal
interaction truth, accessibility, bounded presentation
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
19.1 Command-life-cycle role
At R0/R1, Moana receives only the typed inputs applicable to its role.
Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No underlying effect or credential authority.
22


Chapter 20
Aviator - AVIATOR
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.AVIATOR
Namespace
MJ.PBMEF.Family.AVIATOR.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant AVIATOR
Definition
Organizational workspace, projects, decisions, roles, knowledge, and governed workflow.
Capability
workspace state, decision records
Participant
Aviator
Relationship
Incoming: JO_EXECUTION; outgoing: receipt to MJ/JO
Function
Organizational workspace, projects, decisions, roles, knowledge, and governed workflow.
Expression
Applicable formula set and bounded family receipt
Statement
Aviator contributes its role but cannot substitute for another participant.
Measurement
member purpose, governed records, Bangel Spreadsheets workbooks and reports
Constraint
No root authority, cross-tenant scope, or unadmitted finance.
Annotation
@family(id=’AVIATOR’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant AVIATOR { input; verify; output; boundary; }
Literal
understanding first, organization, decision trace
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
MANIFESTATION
Attribute
full_family_identity=true; self_authority=false
20.1 Command-life-cycle role
At R0/R1, Aviator receives only the typed inputs applicable to its role.
Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No root authority, cross-tenant scope, or unadmitted finance.
23


Chapter 21
CHI - CHI
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.CHI
Namespace
MJ.PBMEF.Family.CHI.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant CHI
Definition
Temporal variance and expected-observed-delivered-reconciled difference state.
Capability
variance object
Participant
CHI
Relationship
Incoming: MJ/root context; outgoing: receipt to MJ/JO
Function
Temporal variance and expected-observed-delivered-reconciled difference state.
Expression
Applicable formula set and bounded family receipt
Statement
CHI contributes its role but cannot substitute for another participant.
Measurement
timestamps, expected/observed states
Constraint
No pricing, punishment, rank, or execution.
Annotation
@family(id=’CHI’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant CHI { input; verify; output; boundary; }
Literal
variance truth, time awareness
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
STATE_ENTITY
Attribute
full_family_identity=true; self_authority=false
21.1 Command-life-cycle role
At R0/R1, CHI receives only the typed inputs applicable to its role. Before N1 it may contribute seman-
tic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may route,
reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its output
becomes part of JO’s final R2 receipt.
Hard boundary
No pricing, punishment, rank, or execution.
24


Chapter 22
WATER - WATER
Construct
Formula-specific expression
Module
MJ.PBMEF.Family.WATER
Namespace
MJ.PBMEF.Family.WATER.Day0
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Authority, MJ.PBMEF.Formulas
Declaration
participant WATER
Definition
Interval uncertainty, verified floor, and bounded unknown-state classification.
Capability
state classification
Participant
WATER
Relationship
Incoming: MJ/root context; outgoing: receipt to MJ/JO
Function
Interval uncertainty, verified floor, and bounded unknown-state classification.
Expression
Applicable formula set and bounded family receipt
Statement
WATER contributes its role but cannot substitute for another participant.
Measurement
measurement intervals, evidence limits
Constraint
No authority or value from classification.
Annotation
@family(id=’WATER’, equal_identity=true, authority_bounded=true)
Directive
produce typed output; preserve unknown; return receipt
Block
participant WATER { input; verify; output; boundary; }
Literal
uncertainty honesty, bounded intervals
Reference
manifest/FAMILY-MANIFESTATION-REGISTER.json
Type
STATE_CLASS
Attribute
full_family_identity=true; self_authority=false
22.1 Command-life-cycle role
At R0/R1, WATER receives only the typed inputs applicable to its role. Before N1 it may contribute
semantic, canonical, physics, verification, prediction, safety, or allocation evidence. After N1 it may
route, reconcile, or prepare a bounded proposal. It cannot issue the final MJ permit unless it is MJ. Its
output becomes part of JO’s final R2 receipt.
Hard boundary
No authority or value from classification.
25


Chapter 23
Governed object verification
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23.1 JP_CAPO
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.JP_CAPO
Namespace
MJ.PBMEF.Object.JP_CAPO.Day0
Declaration
object JP_CAPO
Definition
Canonical math, algorithm, topology, or architecture representation
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Canonical math, algorithm, topology, or architecture representation
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’JP_CAPO’)
Directive
validate schema and provenance before use
Block
object JP_CAPO { fields; invariants; evidence; }
Literal
JP_CAPO
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.2 MK_PHYSICS_CAPO
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.MK_PHYSICS_CAPO
Namespace
MJ.PBMEF.Object.MK_PHYSICS_CAPO.Day0
Declaration
object MK_PHYSICS_CAPO
Definition
Physics applicability, quantities, units, boundaries, equations, uncertainty, and evidence
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Physics applicability, quantities, units, boundaries, equations, uncertainty, and evidence
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’MK_PHYSICS_CAPO’)
Directive
validate schema and provenance before use
Block
object MK_PHYSICS_CAPO { fields; invariants; evidence; }
Literal
MK_PHYSICS_CAPO
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.3 JO_PROOF_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.JO_PROOF_RECEIPT
Namespace
MJ.PBMEF.Object.JO_PROOF_RECEIPT.Day0
Declaration
object JO_PROOF_RECEIPT
Definition
Executed verification result
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Executed verification result
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’JO_PROOF_RECEIPT’)
Directive
validate schema and provenance before use
Block
object JO_PROOF_RECEIPT { fields; invariants; evidence; }
Literal
JO_PROOF_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.4 MJ_PERMIT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.MJ_PERMIT
Namespace
MJ.PBMEF.Object.MJ_PERMIT.Day0
Declaration
object MJ_PERMIT
Definition
Bounded permit decision issued only by MJ
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Bounded permit decision issued only by MJ
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’MJ_PERMIT’)
Directive
validate schema and provenance before use
Block
object MJ_PERMIT { fields; invariants; evidence; }
Literal
MJ_PERMIT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.5 EVE_OBSERVATION
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.EVE_OBSERVATION
Namespace
MJ.PBMEF.Object.EVE_OBSERVATION.Day0
Declaration
object EVE_OBSERVATION
Definition
Variance, screen, capture, egress, or residual evidence
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Variance, screen, capture, egress, or residual evidence
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’EVE_OBSERVATION’)
Directive
validate schema and provenance before use
Block
object EVE_OBSERVATION { fields; invariants; evidence; }
Literal
EVE_OBSERVATION
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.6 M3_ROUTE_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.M3_ROUTE_RECEIPT
Namespace
MJ.PBMEF.Object.M3_ROUTE_RECEIPT.Day0
Declaration
object M3_ROUTE_RECEIPT
Definition
Bounded routing and resource-use receipt
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Bounded routing and resource-use receipt
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’M3_ROUTE_RECEIPT’)
Directive
validate schema and provenance before use
Block
object M3_ROUTE_RECEIPT { fields; invariants; evidence; }
Literal
M3_ROUTE_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.7 MERMAID_ACCOUNT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.MERMAID_ACCOUNT
Namespace
MJ.PBMEF.Object.MERMAID_ACCOUNT.Day0
Declaration
object MERMAID_ACCOUNT
Definition
Accounting, custody, exposure, tax, and reconciliation record
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Accounting, custody, exposure, tax, and reconciliation record
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’MERMAID_ACCOUNT’)
Directive
validate schema and provenance before use
Block
object MERMAID_ACCOUNT { fields; invariants; evidence; }
Literal
MERMAID_ACCOUNT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.8 SHIVA_SHELL
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.SHIVA_SHELL
Namespace
MJ.PBMEF.Object.SHIVA_SHELL.Day0
Declaration
object SHIVA_SHELL
Definition
Governed account envelope for typed financial representations
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Governed account envelope for typed financial representations
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’SHIVA_SHELL’)
Directive
validate schema and provenance before use
Block
object SHIVA_SHELL { fields; invariants; evidence; }
Literal
SHIVA_SHELL
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.9 SHIVAS_INTERNAL_REFLECTION
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.SHIVAS_INTERNAL_REFLECTION
Namespace
MJ.PBMEF.Object.SHIVAS_INTERNAL_REFLECTION.Day0
Declaration
object SHIVAS_INTERNAL_REFLECTION
Definition
Internal non-transferable capital-reflection object
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Internal non-transferable capital-reflection object
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’SHIVAS_INTERNAL_REFLECTION’)
Directive
validate schema and provenance before use
Block
object SHIVAS_INTERNAL_REFLECTION { fields; invariants; evidence; }
Literal
SHIVAS_INTERNAL_REFLECTION
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.10 CHI_VARIANCE_OBJECT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.CHI_VARIANCE_OBJECT
Namespace
MJ.PBMEF.Object.CHI_VARIANCE_OBJECT.Day0
Declaration
object CHI_VARIANCE_OBJECT
Definition
Temporal difference object
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Temporal difference object
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’CHI_VARIANCE_OBJECT’)
Directive
validate schema and provenance before use
Block
object CHI_VARIANCE_OBJECT { fields; invariants; evidence; }
Literal
CHI_VARIANCE_OBJECT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.11 WATER_INTERVAL_STATE
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.WATER_INTERVAL_STATE
Namespace
MJ.PBMEF.Object.WATER_INTERVAL_STATE.Day0
Declaration
object WATER_INTERVAL_STATE
Definition
Uncertainty interval state
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Uncertainty interval state
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’WATER_INTERVAL_STATE’)
Directive
validate schema and provenance before use
Block
object WATER_INTERVAL_STATE { fields; invariants; evidence; }
Literal
WATER_INTERVAL_STATE
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.12 PASSKEY_PUBLIC_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.PASSKEY_PUBLIC_RECEIPT
Namespace
MJ.PBMEF.Object.PASSKEY_PUBLIC_RECEIPT.Day0
Declaration
object PASSKEY_PUBLIC_RECEIPT
Definition
Public verification of founder signature over a bounded content root
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Public verification of founder signature over a bounded content root
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’PASSKEY_PUBLIC_RECEIPT’)
Directive
validate schema and provenance before use
Block
object PASSKEY_PUBLIC_RECEIPT { fields; invariants; evidence; }
Literal
PASSKEY_PUBLIC_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.13 PEARL_VARIANCE_CONTAINER
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.PEARL_VARIANCE_CONTAINER
Namespace
MJ.PBMEF.Object.PEARL_VARIANCE_CONTAINER.Day0
Declaration
object PEARL_VARIANCE_CONTAINER
Definition
Legacy stable ID for a pearl-shaped hypothetical simulation and information-retention object; never a physical container
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Legacy stable ID for a pearl-shaped hypothetical simulation and information-retention object; never a physical container
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’PEARL_VARIANCE_CONTAINER’)
Directive
validate schema and provenance before use
Block
object PEARL_VARIANCE_CONTAINER { fields; invariants; evidence; }
Literal
PEARL_VARIANCE_CONTAINER
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.14 PEARL_ALLOCATION_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.PEARL_ALLOCATION_RECEIPT
Namespace
MJ.PBMEF.Object.PEARL_ALLOCATION_RECEIPT.Day0
Declaration
object PEARL_ALLOCATION_RECEIPT
Definition
M3/JO receipt for simulated Pearl allocation, scenario capacity, source, destination, and lifecycle state; no physical effect
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
M3/JO receipt for simulated Pearl allocation, scenario capacity, source, destination, and lifecycle state; no physical effect
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’PEARL_ALLOCATION_RECEIPT’)
Directive
validate schema and provenance before use
Block
object PEARL_ALLOCATION_RECEIPT { fields; invariants; evidence; }
Literal
PEARL_ALLOCATION_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.15 PEARL_ACOUSTIC_PROFILE
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.PEARL_ACOUSTIC_PROFILE
Namespace
MJ.PBMEF.Object.PEARL_ACOUSTIC_PROFILE.Day0
Declaration
object PEARL_ACOUSTIC_PROFILE
Definition
Hypothetical acoustic simulation profile with declared frequency, medium, observability, uncertainty, and no physical cohesion claim
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Hypothetical acoustic simulation profile with declared frequency, medium, observability, uncertainty, and no physical cohesion claim
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’PEARL_ACOUSTIC_PROFILE’)
Directive
validate schema and provenance before use
Block
object PEARL_ACOUSTIC_PROFILE { fields; invariants; evidence; }
Literal
PEARL_ACOUSTIC_PROFILE
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.16 PEARL_SYMPOSIUM_REGISTRY
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.PEARL_SYMPOSIUM_REGISTRY
Namespace
MJ.PBMEF.Object.PEARL_SYMPOSIUM_REGISTRY.Day0
Declaration
object PEARL_SYMPOSIUM_REGISTRY
Definition
Mermaid/Shiva record of Pearl simulation scenarios, quantities, costs, implications, and regeneration opportunities under MJ
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Mermaid/Shiva record of Pearl simulation scenarios, quantities, costs, implications, and regeneration opportunities under MJ
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’PEARL_SYMPOSIUM_REGISTRY’)
Directive
validate schema and provenance before use
Block
object PEARL_SYMPOSIUM_REGISTRY { fields; invariants; evidence; }
Literal
PEARL_SYMPOSIUM_REGISTRY
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.17 Bangel_SHEET
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.Bangel_SHEET
Namespace
MJ.PBMEF.Object.Bangel_SHEET.Day0
Declaration
object Bangel_SHEET
Definition
Governed spreadsheet-like workbook with immutable revisions, typed cells, dependency graph, and authority scopes
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Governed spreadsheet-like workbook with immutable revisions, typed cells, dependency graph, and authority scopes
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’Bangel_SHEET’)
Directive
validate schema and provenance before use
Block
object Bangel_SHEET { fields; invariants; evidence; }
Literal
Bangel_SHEET
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.18 Bangel_SHEET_CELL
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.Bangel_SHEET_CELL
Namespace
MJ.PBMEF.Object.Bangel_SHEET_CELL.Day0
Declaration
object Bangel_SHEET_CELL
Definition
Typed measurement cell with value, unit, uncertainty, formula, evidence, lineage, and revision
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Typed measurement cell with value, unit, uncertainty, formula, evidence, lineage, and revision
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’Bangel_SHEET_CELL’)
Directive
validate schema and provenance before use
Block
object Bangel_SHEET_CELL { fields; invariants; evidence; }
Literal
Bangel_SHEET_CELL
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.19 Bangel_SHEET_REVISION
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.Bangel_SHEET_REVISION
Namespace
MJ.PBMEF.Object.Bangel_SHEET_REVISION.Day0
Declaration
object Bangel_SHEET_REVISION
Definition
Content-addressed immutable workbook revision and conflict/merge evidence
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Content-addressed immutable workbook revision and conflict/merge evidence
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’Bangel_SHEET_REVISION’)
Directive
validate schema and provenance before use
Block
object Bangel_SHEET_REVISION { fields; invariants; evidence; }
Literal
Bangel_SHEET_REVISION
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.20 Bangel_SHEET_AUDIT_PARTICLE
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.Bangel_SHEET_AUDIT_PARTICLE
Namespace
MJ.PBMEF.Object.Bangel_SHEET_AUDIT_PARTICLE.Day0
Declaration
object Bangel_SHEET_AUDIT_PARTICLE
Definition
Complete audit record for critical spreadsheet edits, formulas, recomputation, and reports
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Complete audit record for critical spreadsheet edits, formulas, recomputation, and reports
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’Bangel_SHEET_AUDIT_PARTICLE’)
Directive
validate schema and provenance before use
Block
object Bangel_SHEET_AUDIT_PARTICLE { fields; invariants; evidence; }
Literal
Bangel_SHEET_AUDIT_PARTICLE
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.21 JPOSMJ_PRODUCT_ENVELOPE
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.JPOSMJ_PRODUCT_ENVELOPE
Namespace
MJ.PBMEF.Object.JPOSMJ_PRODUCT_ENVELOPE.Day0
Declaration
object JPOSMJ_PRODUCT_ENVELOPE
Definition
Portfolio envelope binding JP-origin product logic through MK physics, JO proof, and MJ permit
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Portfolio envelope binding JP-origin product logic through MK physics, JO proof, and MJ permit
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’JPOSMJ_PRODUCT_ENVELOPE’)
Directive
validate schema and provenance before use
Block
object JPOSMJ_PRODUCT_ENVELOPE { fields; invariants; evidence; }
Literal
JPOSMJ_PRODUCT_ENVELOPE
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.22 SISTER_PHYSICAL_CONTAINMENT_PROFILE
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.SISTER_PHYSICAL_CONTAINMENT_PROFILE
Namespace
MJ.PBMEF.Object.SISTER_PHYSICAL_CONTAINMENT_PROFILE.Day0
Declaration
object SISTER_PHYSICAL_CONTAINMENT_PROFILE
Definition
Pre-Pearl physical umbrella/descent/containment profile with normalized topology and profile-specific unknown physical size/capacity
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Pre-Pearl physical umbrella/descent/containment profile with normalized topology and profile-specific unknown physical size/capacity
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’SISTER_PHYSICAL_CONTAINMENT_PROFILE’)
Directive
validate schema and provenance before use
Block
object SISTER_PHYSICAL_CONTAINMENT_PROFILE { fields; invariants; evidence; }
Literal
SISTER_PHYSICAL_CONTAINMENT_PROFILE
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.23 STANDARD_CONTAINMENT_GEOMETRY_PROFILE
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.STANDARD_CONTAINMENT_GEOMETRY_PROFILE
Namespace
MJ.PBMEF.Object.STANDARD_CONTAINMENT_GEOMETRY_PROFILE.Day0
Declaration
object STANDARD_CONTAINMENT_GEOMETRY_PROFILE
Definition
Typed scale-independent rectangle/cone/umbrella/descent/EVE/reservoir geometry and modification parameters
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Typed scale-independent rectangle/cone/umbrella/descent/EVE/reservoir geometry and modification parameters
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’STANDARD_CONTAINMENT_GEOMETRY_PROFILE’)
Directive
validate schema and provenance before use
Block
object STANDARD_CONTAINMENT_GEOMETRY_PROFILE { fields; invariants; evidence; }
Literal
STANDARD_CONTAINMENT_GEOMETRY_PROFILE
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.24 REFERENCE_GAS_PROFILE_H2
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.REFERENCE_GAS_PROFILE_H2
Namespace
MJ.PBMEF.Object.REFERENCE_GAS_PROFILE_H2.Day0
Declaration
object REFERENCE_GAS_PROFILE_H2
Definition
H2 equation/reference profile for density, equivalent volume, observed gas height, and motion calculations; no physical use authority
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
H2 equation/reference profile for density, equivalent volume, observed gas height, and motion calculations; no physical use authority
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’REFERENCE_GAS_PROFILE_H2’)
Directive
validate schema and provenance before use
Block
object REFERENCE_GAS_PROFILE_H2 { fields; invariants; evidence; }
Literal
REFERENCE_GAS_PROFILE_H2
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.25 CONTAINMENT_MODIFICATION_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.CONTAINMENT_MODIFICATION_RECEIPT
Namespace
MJ.PBMEF.Object.CONTAINMENT_MODIFICATION_RECEIPT.Day0
Declaration
object CONTAINMENT_MODIFICATION_RECEIPT
Definition
Recalculation and revalidation receipt for command/profile-specific geometry changes
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Recalculation and revalidation receipt for command/profile-specific geometry changes
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’CONTAINMENT_MODIFICATION_RECEIPT’)
Directive
validate schema and provenance before use
Block
object CONTAINMENT_MODIFICATION_RECEIPT { fields; invariants; evidence; }
Literal
CONTAINMENT_MODIFICATION_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.26 CONE_TOP_PEARL_ANCHOR
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.CONE_TOP_PEARL_ANCHOR
Namespace
MJ.PBMEF.Object.CONE_TOP_PEARL_ANCHOR.Day0
Declaration
object CONE_TOP_PEARL_ANCHOR
Definition
Hypothetical information coordinate at the top-of-cone observation plane; no physical placement
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Hypothetical information coordinate at the top-of-cone observation plane; no physical placement
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’CONE_TOP_PEARL_ANCHOR’)
Directive
validate schema and provenance before use
Block
object CONE_TOP_PEARL_ANCHOR { fields; invariants; evidence; }
Literal
CONE_TOP_PEARL_ANCHOR
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.27 GAS_HEIGHT_OBSERVATION
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.GAS_HEIGHT_OBSERVATION
Namespace
MJ.PBMEF.Object.GAS_HEIGHT_OBSERVATION.Day0
Declaration
object GAS_HEIGHT_OBSERVATION
Definition
Calibrated pressure/temperature/density/height/time observation for gas-front reference calculations
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Calibrated pressure/temperature/density/height/time observation for gas-front reference calculations
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’GAS_HEIGHT_OBSERVATION’)
Directive
validate schema and provenance before use
Block
object GAS_HEIGHT_OBSERVATION { fields; invariants; evidence; }
Literal
GAS_HEIGHT_OBSERVATION
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.28 RESERVOIR_RETURN_LOOP_PROFILE
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.RESERVOIR_RETURN_LOOP_PROFILE
Namespace
MJ.PBMEF.Object.RESERVOIR_RETURN_LOOP_PROFILE.Day0
Declaration
object RESERVOIR_RETURN_LOOP_PROFILE
Definition
Typed rear outlet, external reservoir, and circular reentry geometry/profile.
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Typed rear outlet, external reservoir, and circular reentry geometry/profile.
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’RESERVOIR_RETURN_LOOP_PROFILE’)
Directive
validate schema and provenance before use
Block
object RESERVOIR_RETURN_LOOP_PROFILE { fields; invariants; evidence; }
Literal
RESERVOIR_RETURN_LOOP_PROFILE
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.29 OUTWARD_GAP_PATH_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.OUTWARD_GAP_PATH_RECEIPT
Namespace
MJ.PBMEF.Object.OUTWARD_GAP_PATH_RECEIPT.Day0
Declaration
object OUTWARD_GAP_PATH_RECEIPT
Definition
JO/MK proof that the outlet path remains outside the nonphysical Pearl reference circle.
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
JO/MK proof that the outlet path remains outside the nonphysical Pearl reference circle.
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’OUTWARD_GAP_PATH_RECEIPT’)
Directive
validate schema and provenance before use
Block
object OUTWARD_GAP_PATH_RECEIPT { fields; invariants; evidence; }
Literal
OUTWARD_GAP_PATH_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.30 RESERVOIR_BUFFER_ACCOUNT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.RESERVOIR_BUFFER_ACCOUNT
Namespace
MJ.PBMEF.Object.RESERVOIR_BUFFER_ACCOUNT.Day0
Declaration
object RESERVOIR_BUFFER_ACCOUNT
Definition
EVE/Mermaid typed balance of admitted, returned, drained, escaped, and retained quantities.
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
EVE/Mermaid typed balance of admitted, returned, drained, escaped, and retained quantities.
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’RESERVOIR_BUFFER_ACCOUNT’)
Directive
validate schema and provenance before use
Block
object RESERVOIR_BUFFER_ACCOUNT { fields; invariants; evidence; }
Literal
RESERVOIR_BUFFER_ACCOUNT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.31 CIRCULAR_REENTRY_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.CIRCULAR_REENTRY_RECEIPT
Namespace
MJ.PBMEF.Object.CIRCULAR_REENTRY_RECEIPT.Day0
Declaration
object CIRCULAR_REENTRY_RECEIPT
Definition
Circular port, inward angle, tangential component, continuity, and spiral-compatibility evidence.
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Circular port, inward angle, tangential component, continuity, and spiral-compatibility evidence.
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’CIRCULAR_REENTRY_RECEIPT’)
Directive
validate schema and provenance before use
Block
object CIRCULAR_REENTRY_RECEIPT { fields; invariants; evidence; }
Literal
CIRCULAR_REENTRY_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.32 RELATIVE_FRAME_FRICTION_LEDGER
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.RELATIVE_FRAME_FRICTION_LEDGER
Namespace
MJ.PBMEF.Object.RELATIVE_FRAME_FRICTION_LEDGER.Day0
Declaration
object RELATIVE_FRAME_FRICTION_LEDGER
Definition
MK/JO/Mermaid record of frame-relative velocity, dissipation, and any bounded recoverable-energy claim.
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
MK/JO/Mermaid record of frame-relative velocity, dissipation, and any bounded recoverable-energy claim.
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’RELATIVE_FRAME_FRICTION_LEDGER’)
Directive
validate schema and provenance before use
Block
object RELATIVE_FRAME_FRICTION_LEDGER { fields; invariants; evidence; }
Literal
RELATIVE_FRAME_FRICTION_LEDGER
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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23.33 RESERVOIR_LAKE_BUFFER
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.RESERVOIR_LAKE_BUFFER
Namespace
MJ.PBMEF.Object.RESERVOIR_LAKE_BUFFER.Day0
Declaration
object RESERVOIR_LAKE_BUFFER
Definition
Bounded post-containment buffer candidate for retention, redistribution, and receipted re-entry
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Bounded post-containment buffer candidate for retention, redistribution, and receipted re-entry
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’RESERVOIR_LAKE_BUFFER’)
Directive
validate schema and provenance before use
Block
object RESERVOIR_LAKE_BUFFER { fields; invariants; evidence; }
Literal
RESERVOIR_LAKE_BUFFER
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.34 BACKSIDE_OUTLET_PORT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.BACKSIDE_OUTLET_PORT
Namespace
MJ.PBMEF.Object.BACKSIDE_OUTLET_PORT.Day0
Declaration
object BACKSIDE_OUTLET_PORT
Definition
High backside outlet candidate located below containment maximum height
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
High backside outlet candidate located below containment maximum height
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’BACKSIDE_OUTLET_PORT’)
Directive
validate schema and provenance before use
Block
object BACKSIDE_OUTLET_PORT { fields; invariants; evidence; }
Literal
BACKSIDE_OUTLET_PORT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
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PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper V - Family / Objects
23.35 OUTWARD_GAP_ARC
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.OUTWARD_GAP_ARC
Namespace
MJ.PBMEF.Object.OUTWARD_GAP_ARC.Day0
Declaration
object OUTWARD_GAP_ARC
Definition
Outward-facing angular reference through which the outlet clears the nonphysical Pearl reference circle
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Outward-facing angular reference through which the outlet clears the nonphysical Pearl reference circle
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’OUTWARD_GAP_ARC’)
Directive
validate schema and provenance before use
Block
object OUTWARD_GAP_ARC { fields; invariants; evidence; }
Literal
OUTWARD_GAP_ARC
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.36 PEARL_REFERENCE_CIRCLE
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.PEARL_REFERENCE_CIRCLE
Namespace
MJ.PBMEF.Object.PEARL_REFERENCE_CIRCLE.Day0
Declaration
object PEARL_REFERENCE_CIRCLE
Definition
Hypothetical simulation/measurement circle used for path-clearance calculations; no physical wall or capacity
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Hypothetical simulation/measurement circle used for path-clearance calculations; no physical wall or capacity
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’PEARL_REFERENCE_CIRCLE’)
Directive
validate schema and provenance before use
Block
object PEARL_REFERENCE_CIRCLE { fields; invariants; evidence; }
Literal
PEARL_REFERENCE_CIRCLE
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
Page 44 of 46


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper V - Family / Objects
23.37 CIRCULAR_REENTRY_PORT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.CIRCULAR_REENTRY_PORT
Namespace
MJ.PBMEF.Object.CIRCULAR_REENTRY_PORT.Day0
Declaration
object CIRCULAR_REENTRY_PORT
Definition
Circular inward-angled port candidate supplying measured radial and tangential re-entry components
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Circular inward-angled port candidate supplying measured radial and tangential re-entry components
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’CIRCULAR_REENTRY_PORT’)
Directive
validate schema and provenance before use
Block
object CIRCULAR_REENTRY_PORT { fields; invariants; evidence; }
Literal
CIRCULAR_REENTRY_PORT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
23.38 RESERVOIR_TRANSFER_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.RESERVOIR_TRANSFER_RECEIPT
Namespace
MJ.PBMEF.Object.RESERVOIR_TRANSFER_RECEIPT.Day0
Declaration
object RESERVOIR_TRANSFER_RECEIPT
Definition
Per-transaction outlet/lake/re-entry/cycle/participant evidence receipt
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Per-transaction outlet/lake/re-entry/cycle/participant evidence receipt
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’RESERVOIR_TRANSFER_RECEIPT’)
Directive
validate schema and provenance before use
Block
object RESERVOIR_TRANSFER_RECEIPT { fields; invariants; evidence; }
Literal
RESERVOIR_TRANSFER_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
Page 45 of 46


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper V - Family / Objects
23.39 PERSPECTIVE_FRICTION_RECEIPT
Construct
Formula-specific expression
Module
MJ.PBMEF.Object.PERSPECTIVE_FRICTION_RECEIPT
Namespace
MJ.PBMEF.Object.PERSPECTIVE_FRICTION_RECEIPT.Day0
Declaration
object PERSPECTIVE_FRICTION_RECEIPT
Definition
Separates coordinate-transform residual, physical dissipation, and information friction
Capability
Represent, retain, route, reconcile, or evidence only as declared
Participant
Bound participants determined by object role
Relationship
Referenced by JP/MK/JO and applicable family manifestations
Function
Separates coordinate-transform residual, physical dissipation, and information friction
Expression
Typed object fields and invariant predicates
Statement
Object identity is not authority.
Measurement
Only when fields include valid quantity, units, boundary, time, and uncertainty
Constraint
authority=false; no self-admission
Annotation
@object(id=’PERSPECTIVE_FRICTION_RECEIPT’)
Directive
validate schema and provenance before use
Block
object PERSPECTIVE_FRICTION_RECEIPT { fields; invariants; evidence; }
Literal
PERSPECTIVE_FRICTION_RECEIPT
Reference
manifest/FAMILY-OBJECT-REGISTER.json
Type
GOVERNED_OBJECT
Attribute
authority=false
Page 46 of 46


MJ-PBMEF Pink Paper - Volume VI
Product Manifestations, White-Paper Lineage, and Verification Crosswalk
Michael Bangel - Author and Architect
August 2026


Contents
1
Product gateway verification
5
2
MJ Physics Based Measurement Engineering Framework - PBMEF-CORE
6
2.1 Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
3
Bangel Governed Measurement Language - Bangel-LANGUAGE
7
3.1 Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
4
Elsa Deterministic Semantic Recovery - ELSA-SEMANTICS
8
4.1 Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
5
JP Mathematical and Architectural Canon - JP-CANON
9
5.1 Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
6
Mika/MK Physics Modulator System - MK-PHYSICS
10
6.1 Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
7
JO Deterministic Proof and Runtime - JO-RUNTIME
11
7.1 Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
8
MJOS Operating Substrate - MJOS-SUBSTRATE
12
8.1 Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
9
JP Semiconductor Phone Battery and OS Candidate - JP-SC-PHONE
13
9.1 Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
10JP Large-Scale Boating Power Candidate - JP-LS-BOAT
14
10.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
11JP Peaceful High-Energy Propulsion Research Candidate - JP-PEACEFUL-PROPULSION
15
11.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
12Sister Predictive Containment System - SISTER-CONTAINMENT
16
12.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
13EVE Variance Screen and Egress Accounting - EVE-SCREEN
17
13.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
14Angels Safety and Corrective Command System - ANGELS-SAFETY
18
14.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
15Mermaid Accounting and Reconciliation System - MERMAID-RECON
19
15.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
16Shiva Dual Financial Rails - SHIVA-RAILS
20
16.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
1


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
17SHIVAS Internal Settlement Reflection - SHIVAS-INTERNAL
21
17.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
18Shiva Crypto External-Market Candidate - SHIVA-CRYPTO
22
18.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
19Shiva Exchange Rule Reference - SHIVA-EXCHANGE
23
19.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
20Moana Governed Browser - MOANA-BROWSER
24
20.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
21Aviator Organizational Workspace - AVIATOR-WORKSPACE
25
21.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
22Lecanto Truthful Visualization - LECANTO-VISUAL
26
22.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
23Elsa Governed Marketplace Reference - ELSA-MARKETPLACE
27
23.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
24Shekina Distributed Continuity - SHEKINA-CONTINUITY
28
24.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
25Pearl Hypothetical Simulation and Information-Retention System - PEARL-CONTAINMENT
29
25.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
26Bangel Spreadsheets - Bangel-SPREADSHEETS
30
26.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
27JPOSMJ Product Portfolio Envelope - JPOSMJ-PORTFOLIO
31
27.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
28MJ Standard Containment Geometry and Reference Gas Model - STANDARD-CONTAINMENT-
GEOMETRY
32
28.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
29MJ Reservoir Collection,
Lake Buffer,
and Spiral-Compatible Re-entry - RESERVOIR-
COLLECTION-MODULATION
33
29.1Application and life-cycle potential
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
30Registered white-paper verification crosswalk
34
30.1MJ — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-01
. . . . . . . . . . . . . . . .
35
30.2Bangel — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-02
. . . . . . . . . . . . . .
35
30.3Elsa — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-03
. . . . . . . . . . . . . . .
36
30.4JP — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-04 . . . . . . . . . . . . . . . . .
36
30.5Mika / MK — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-05
. . . . . . . . . . . .
37
30.6JO — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-06 . . . . . . . . . . . . . . . . .
37
30.7MJOS — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-07 . . . . . . . . . . . . . . .
38
30.8Angels — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-08
. . . . . . . . . . . . . .
38
30.9Bellatrix — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-09
. . . . . . . . . . . . .
39
30.10Sister — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-10 . . . . . . . . . . . . . . .
39
30.11EVE — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-11
. . . . . . . . . . . . . . .
40
30.12Mary / M3 — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-12
. . . . . . . . . . . .
40
30.13Mermaid — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-13 . . . . . . . . . . . . .
41
30.14Shiva — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-14 . . . . . . . . . . . . . . .
41
30.15Shekina — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-15
. . . . . . . . . . . . .
42
30.16Belle — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-16
. . . . . . . . . . . . . . .
42
30.17Lecanto — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-17
. . . . . . . . . . . . .
43
30.18Moana — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-18
. . . . . . . . . . . . . .
43
30.19Aviator — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-19 . . . . . . . . . . . . . .
44
Page 2 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.20CHI — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-20 . . . . . . . . . . . . . . . .
44
30.21WATER — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-21 . . . . . . . . . . . . . .
45
30.22MJ Physics Based Measurement Engineering Framework - MJ-PBMEF-PRODUCT-WP-01
. . . .
45
30.23Bangel Governed Measurement Language - MJ-PBMEF-PRODUCT-WP-02 . . . . . . . . . . . . .
46
30.24Elsa Deterministic Semantic Recovery - MJ-PBMEF-PRODUCT-WP-03
. . . . . . . . . . . . . .
46
30.25JP Mathematical and Architectural Canon - MJ-PBMEF-PRODUCT-WP-04 . . . . . . . . . . . . .
47
30.26Mika/MK Physics Modulator System - MJ-PBMEF-PRODUCT-WP-05 . . . . . . . . . . . . . . . .
47
30.27JO Deterministic Proof and Runtime - MJ-PBMEF-PRODUCT-WP-06 . . . . . . . . . . . . . . . .
48
30.28MJOS Operating Substrate - MJ-PBMEF-PRODUCT-WP-07 . . . . . . . . . . . . . . . . . . . . .
48
30.29JP Semiconductor Phone Battery and OS Candidate - MJ-PBMEF-PRODUCT-WP-08
. . . . . . .
49
30.30JP Large-Scale Boating Power Candidate - MJ-PBMEF-PRODUCT-WP-09
. . . . . . . . . . . . .
49
30.31JP Peaceful High-Energy Propulsion Research Candidate - MJ-PBMEF-PRODUCT-WP-10
. . . .
50
30.32Sister Predictive Containment System - MJ-PBMEF-PRODUCT-WP-11 . . . . . . . . . . . . . . .
50
30.33EVE Variance Screen and Egress Accounting - MJ-PBMEF-PRODUCT-WP-12 . . . . . . . . . . .
51
30.34Angels Safety and Corrective Command System - MJ-PBMEF-PRODUCT-WP-13
. . . . . . . . .
51
30.35Mermaid Accounting and Reconciliation System - MJ-PBMEF-PRODUCT-WP-14
. . . . . . . . .
52
30.36Shiva Dual Financial Rails - MJ-PBMEF-PRODUCT-WP-15
. . . . . . . . . . . . . . . . . . . . .
52
30.37SHIVAS Internal Settlement Reflection - MJ-PBMEF-PRODUCT-WP-16
. . . . . . . . . . . . . .
53
30.38Shiva Crypto External-Market Candidate - MJ-PBMEF-PRODUCT-WP-17
. . . . . . . . . . . . .
53
30.39Shiva Exchange Rule Reference - MJ-PBMEF-PRODUCT-WP-18 . . . . . . . . . . . . . . . . . .
54
30.40Moana Governed Browser - MJ-PBMEF-PRODUCT-WP-19
. . . . . . . . . . . . . . . . . . . . .
54
30.41Aviator Organizational Workspace - MJ-PBMEF-PRODUCT-WP-20 . . . . . . . . . . . . . . . . .
55
30.42Lecanto Truthful Visualization - MJ-PBMEF-PRODUCT-WP-21 . . . . . . . . . . . . . . . . . . .
55
30.43Elsa Governed Marketplace Reference - MJ-PBMEF-PRODUCT-WP-22
. . . . . . . . . . . . . .
56
30.44Shekina Distributed Continuity - MJ-PBMEF-PRODUCT-WP-23
. . . . . . . . . . . . . . . . . .
56
30.45Pearl Hypothetical Simulation and Information-Retention System - MJ-PBMEF-PRODUCT-WP-24 57
30.46Bangel Spreadsheets - MJ-PBMEF-PRODUCT-WP-25
. . . . . . . . . . . . . . . . . . . . . . . .
57
30.47JPOSMJ Product Portfolio Envelope - MJ-PBMEF-PRODUCT-WP-26
. . . . . . . . . . . . . . . .
58
30.48MJ Standard Containment Geometry and Reference Gas Model - MJ-PBMEF-PRODUCT-WP-27 .
58
30.49MJ Reservoir Collection Modulation and Return Loop - MJ-PBMEF-PRODUCT-WP-28
. . . . . .
59
30.50R1 and R2 State Representation - MJ-PBMEF-REPRESENTATION-WP-01 . . . . . . . . . . . . . .
59
30.51Noise Floor and 23 mg Inflection - MJ-PBMEF-REPRESENTATION-WP-02
. . . . . . . . . . . . .
60
30.52Upward 3x3 Node and Umbrella Representation - MJ-PBMEF-REPRESENTATION-WP-03 . . . . .
60
30.53Memory, Request Occultation, and Generational Handoff - MJ-PBMEF-REPRESENTATION-WP-04
61
30.54Static Intake and Energy-Wake Representation - MJ-PBMEF-REPRESENTATION-WP-05
. . . . .
61
30.55EVE Variance, Screen, Evaporation, and Egress - MJ-PBMEF-REPRESENTATION-WP-06 . . . . .
62
30.56Shiva and Mermaid Financial Rails - MJ-PBMEF-REPRESENTATION-WP-07 . . . . . . . . . . . .
62
30.57Passkey, Claims Ceiling, and Repository Authentication - MJ-PBMEF-REPRESENTATION-WP-08 .
63
30.58Pearl
Hypothetical
Geometry
and
Acoustic
Simulation
Representation
-
MJ-PBMEF-
REPRESENTATION-WP-09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
30.59Bangel Spreadsheets Cell, Dependency, Revision, and Pearl Simulation Field - MJ-PBMEF-
REPRESENTATION-WP-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
30.60Standard
Containment
Geometry
and
H2
Reference
Representation
-
MJ-PBMEF-
REPRESENTATION-WP-11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
30.61Reservoir Return Loop Physics Representation - MJ-PBMEF-REPRESENTATION-WP-12
. . . . .
65
Document control
Project
MJ: Physics Based Measurement Engineering Framework
Project ID
MJ-PBMEF-001
Source build
MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE
Document ID
MJ-PBMEF-PINK-PAPER-001/VOL-VI
Author and architect
Michael Bangel
Status
FOUNDER_REVIEW_CANDIDATE_PENDING_FREEZE
Scope
All products and registered white papers mapped into the gateway
lifecycle.
Page 3 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
Claims ceiling
This document is a private pre-Day-0 review and verification candidate. It authenticates no pri-
vate key and creates no physical validation, physical operation authority, product certification,
external regulatory authority, production deployment, financial-product launch, token issuance,
AI integration, or physical-coordinate approval. Formula pages distinguish mathematical validity,
reference implementation, simulation, measured evidence, authority, and execution.
Page 4 of 65


Chapter 1
Product gateway verification
5


Chapter 2
MJ Physics Based Measurement Engi-
neering Framework - PBMEF-CORE
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.PBMEF-CORE
Namespace
MJ.PBMEF.Product.PBMEF-CORE.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product PBMEF-CORE
Definition
Integrate purpose, mathematics, physics, verification, safety, resource routing, accounting, finance, evidence, and bounded permit decisions.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Integrate purpose, mathematics, physics, verification, safety, resource routing, accounting, finance, evidence, and bounded permit decisions.
Expression
Product-specific composition of formula and object records
Statement
Status: DAY0_PREPASSKEY_COMPLETE_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’PBMEF-CORE’, class=’CORE_FRAMEWORK’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product PBMEF-CORE { purpose; formulas; families; evidence; permit; }
Literal
PBMEF-CORE
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
CORE_FRAMEWORK
Attribute
status=DAY0_PREPASSKEY_COMPLETE_CANDIDATE
2.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
6


Chapter 3
Bangel
Governed
Measurement
Lan-
guage - Bangel-LANGUAGE
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.Bangel-LANGUAGE
Namespace
MJ.PBMEF.Product.Bangel-LANGUAGE.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product Bangel-LANGUAGE
Definition
Express human purpose, typed measurements, formulas, evidence, and command pathways.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Express human purpose, typed measurements, formulas, evidence, and command pathways.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’Bangel-LANGUAGE’, class=’LANGUAGE’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product Bangel-LANGUAGE { purpose; formulas; families; evidence; permit; }
Literal
Bangel-LANGUAGE
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
LANGUAGE
Attribute
status=SPECIFICATION_CANDIDATE
3.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
7


Chapter 4
Elsa Deterministic Semantic Recovery -
ELSA-SEMANTICS
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.ELSA-SEMANTICS
Namespace
MJ.PBMEF.Product.ELSA-SEMANTICS.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product ELSA-SEMANTICS
Definition
Recover and preserve declared meaning without autonomous inference or authority.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Recover and preserve declared meaning without autonomous inference or authority.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’ELSA-SEMANTICS’, class=’SEMANTIC_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product ELSA-SEMANTICS { purpose; formulas; families; evidence; permit; }
Literal
ELSA-SEMANTICS
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
SEMANTIC_SYSTEM
Attribute
status=SPECIFICATION_CANDIDATE
4.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
8


Chapter 5
JP
Mathematical
and
Architectural
Canon - JP-CANON
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.JP-CANON
Namespace
MJ.PBMEF.Product.JP-CANON.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product JP-CANON
Definition
Represent equations, algorithms, CAPOs, topology, products, and proofs.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Represent equations, algorithms, CAPOs, topology, products, and proofs.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’JP-CANON’, class=’CANONICAL_REPRESENTATION’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product JP-CANON { purpose; formulas; families; evidence; permit; }
Literal
JP-CANON
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
CANONICAL_REPRESENTATION
Attribute
status=SPECIFICATION_CANDIDATE
5.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
9


Chapter 6
Mika/MK Physics Modulator System -
MK-PHYSICS
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.MK-PHYSICS
Namespace
MJ.PBMEF.Product.MK-PHYSICS.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product MK-PHYSICS
Definition
Create physics representations and verify units, conservation, boundaries, scale, and evidence ceilings.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Create physics representations and verify units, conservation, boundaries, scale, and evidence ceilings.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_IMPLEMENTATION
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’MK-PHYSICS’, class=’PHYSICS_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product MK-PHYSICS { purpose; formulas; families; evidence; permit; }
Literal
MK-PHYSICS
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
PHYSICS_SYSTEM
Attribute
status=REFERENCE_IMPLEMENTATION
6.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
10


Chapter 7
JO Deterministic Proof and Runtime -
JO-RUNTIME
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.JO-RUNTIME
Namespace
MJ.PBMEF.Product.JO-RUNTIME.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product JO-RUNTIME
Definition
Verify types, units, authority, physics, tests, evidence, and bounded execution.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Verify types, units, authority, physics, tests, evidence, and bounded execution.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_IMPLEMENTATION
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’JO-RUNTIME’, class=’RUNTIME’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product JO-RUNTIME { purpose; formulas; families; evidence; permit; }
Literal
JO-RUNTIME
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
RUNTIME
Attribute
status=REFERENCE_IMPLEMENTATION
7.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
11


Chapter 8
MJOS
Operating
Substrate
-
MJOS-
SUBSTRATE
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.MJOS-SUBSTRATE
Namespace
MJ.PBMEF.Product.MJOS-SUBSTRATE.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product MJOS-SUBSTRATE
Definition
Provide isolated resources, memory, storage, network, scheduling, and continuity under MJ leases.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Provide isolated resources, memory, storage, network, scheduling, and continuity under MJ leases.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’MJOS-SUBSTRATE’, class=’OPERATING_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product MJOS-SUBSTRATE { purpose; formulas; families; evidence; permit; }
Literal
MJOS-SUBSTRATE
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
OPERATING_SYSTEM
Attribute
status=SPECIFICATION_CANDIDATE
8.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
12


Chapter 9
JP Semiconductor Phone Battery and OS
Candidate - JP-SC-PHONE
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.JP-SC-PHONE
Namespace
MJ.PBMEF.Product.JP-SC-PHONE.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product JP-SC-PHONE
Definition
Explore semiconductor-scale static intake, power wake, solar assist, battery, and operating-system integration.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
JP and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Explore semiconductor-scale static intake, power wake, solar assist, battery, and operating-system integration.
Expression
Product-specific composition of formula and object records
Statement
Status: PLANNED_ONLY_NO_PHYSICAL_ARTICLE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’JP-SC-PHONE’, class=’PHYSICAL_PRODUCT_CANDIDATE’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product JP-SC-PHONE { purpose; formulas; families; evidence; permit; }
Literal
JP-SC-PHONE
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
PHYSICAL_PRODUCT_CANDIDATE
Attribute
status=PLANNED_ONLY_NO_PHYSICAL_ARTICLE
9.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
13


Chapter 10
JP Large-Scale Boating Power Candi-
date - JP-LS-BOAT
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.JP-LS-BOAT
Namespace
MJ.PBMEF.Product.JP-LS-BOAT.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product JP-LS-BOAT
Definition
Explore large-scale static intake, solar initiation, power bus, containment, and marine power integration.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
JP and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Explore large-scale static intake, solar initiation, power bus, containment, and marine power integration.
Expression
Product-specific composition of formula and object records
Statement
Status: PLANNED_ONLY_UNCLASSIFIED
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’JP-LS-BOAT’, class=’PHYSICAL_PRODUCT_CANDIDATE’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product JP-LS-BOAT { purpose; formulas; families; evidence; permit; }
Literal
JP-LS-BOAT
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
PHYSICAL_PRODUCT_CANDIDATE
Attribute
status=PLANNED_ONLY_UNCLASSIFIED
10.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
14


Chapter 11
JP
Peaceful
High-Energy
Propulsion
Research
Candidate
-
JP-PEACEFUL-
PROPULSION
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.JP-PEACEFUL-PROPULSION
Namespace
MJ.PBMEF.Product.JP-PEACEFUL-PROPULSION.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product JP-PEACEFUL-PROPULSION
Definition
Explore peaceful propulsion measurement and control under non-weaponization, safety, and regulatory gates.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
JP and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Explore peaceful propulsion measurement and control under non-weaponization, safety, and regulatory gates.
Expression
Product-specific composition of formula and object records
Statement
Status: PLANNED_ONLY_SAFETY_HOLD
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’JP-PEACEFUL-PROPULSION’, class=’HIGH_RISK_PHYSICAL_RESEARCH_CANDIDATE’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product JP-PEACEFUL-PROPULSION { purpose; formulas; families; evidence; permit; }
Literal
JP-PEACEFUL-PROPULSION
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
HIGH_RISK_PHYSICAL_RESEARCH_CANDIDATE
Attribute
status=PLANNED_ONLY_SAFETY_HOLD
11.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
15


Chapter 12
Sister Predictive Containment System -
SISTER-CONTAINMENT
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.SISTER-CONTAINMENT
Namespace
MJ.PBMEF.Product.SISTER-CONTAINMENT.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product SISTER-CONTAINMENT
Definition
Predict demand, allocate buffers, detect anomalies, and stage overflow in bounded umbrellas.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Predict demand, allocate buffers, detect anomalies, and stage overflow in bounded umbrellas.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’SISTER-CONTAINMENT’, class=’PREDICTION_AND_CONTAINMENT’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product SISTER-CONTAINMENT { purpose; formulas; families; evidence; permit; }
Literal
SISTER-CONTAINMENT
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
PREDICTION_AND_CONTAINMENT
Attribute
status=SPECIFICATION_CANDIDATE
12.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
16


Chapter 13
EVE Variance Screen and Egress Ac-
counting - EVE-SCREEN
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.EVE-SCREEN
Namespace
MJ.PBMEF.Product.EVE-SCREEN.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product EVE-SCREEN
Definition
Account for variance, evaporation, leakage, capture, and natural egress without silent loss.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Account for variance, evaporation, leakage, capture, and natural egress without silent loss.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’EVE-SCREEN’, class=’MEASUREMENT_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product EVE-SCREEN { purpose; formulas; families; evidence; permit; }
Literal
EVE-SCREEN
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
MEASUREMENT_SYSTEM
Attribute
status=SPECIFICATION_CANDIDATE
13.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
17


Chapter 14
Angels Safety and Corrective Command
System - ANGELS-SAFETY
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.ANGELS-SAFETY
Namespace
MJ.PBMEF.Product.ANGELS-SAFETY.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product ANGELS-SAFETY
Definition
Provide domain-bounded telemetry, hold, denial, isolation, and corrective protocols.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Provide domain-bounded telemetry, hold, denial, isolation, and corrective protocols.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’ANGELS-SAFETY’, class=’SAFETY_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product ANGELS-SAFETY { purpose; formulas; families; evidence; permit; }
Literal
ANGELS-SAFETY
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
SAFETY_SYSTEM
Attribute
status=SPECIFICATION_CANDIDATE
14.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
18


Chapter 15
Mermaid Accounting and Reconciliation
System - MERMAID-RECON
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.MERMAID-RECON
Namespace
MJ.PBMEF.Product.MERMAID-RECON.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product MERMAID-RECON
Definition
Maintain balances, custody evidence, exposure, tax lots, statements, and reconciliation.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Maintain balances, custody evidence, exposure, tax lots, statements, and reconciliation.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’MERMAID-RECON’, class=’ACCOUNTING_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product MERMAID-RECON { purpose; formulas; families; evidence; permit; }
Literal
MERMAID-RECON
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
ACCOUNTING_SYSTEM
Attribute
status=SPECIFICATION_CANDIDATE
15.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
19


Chapter 16
Shiva Dual Financial Rails - SHIVA-RAILS
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.SHIVA-RAILS
Namespace
MJ.PBMEF.Product.SHIVA-RAILS.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product SHIVA-RAILS
Definition
Separate stability/cash functions from investment and crypto risk while preserving liquidity-first ethics.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Separate stability/cash functions from investment and crypto risk while preserving liquidity-first ethics.
Expression
Product-specific composition of formula and object records
Statement
Status: INTERNAL_MODEL_EXTERNAL_DISABLED
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’SHIVA-RAILS’, class=’FINANCIAL_REFERENCE_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product SHIVA-RAILS { purpose; formulas; families; evidence; permit; }
Literal
SHIVA-RAILS
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
FINANCIAL_REFERENCE_SYSTEM
Attribute
status=INTERNAL_MODEL_EXTERNAL_DISABLED
16.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
20


Chapter 17
SHIVAS Internal Settlement Reflection -
SHIVAS-INTERNAL
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.SHIVAS-INTERNAL
Namespace
MJ.PBMEF.Product.SHIVAS-INTERNAL.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product SHIVAS-INTERNAL
Definition
Represent internal capital reflections without minting, redemption, public offer, or value guarantee.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
SHIVA and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Represent internal capital reflections without minting, redemption, public offer, or value guarantee.
Expression
Product-specific composition of formula and object records
Statement
Status: NONTRANSFERABLE_NO_MONETARY_VALUE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’SHIVAS-INTERNAL’, class=’CAPITAL_REFLECTION_OBJECT’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product SHIVAS-INTERNAL { purpose; formulas; families; evidence; permit; }
Literal
SHIVAS-INTERNAL
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
CAPITAL_REFLECTION_OBJECT
Attribute
status=NONTRANSFERABLE_NO_MONETARY_VALUE
17.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
21


Chapter 18
Shiva
Crypto
External-Market
Candi-
date - SHIVA-CRYPTO
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.SHIVA-CRYPTO
Namespace
MJ.PBMEF.Product.SHIVA-CRYPTO.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product SHIVA-CRYPTO
Definition
Model a separately governed external crypto rail subject to full classification and authorization.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
SHIVA and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Model a separately governed external crypto rail subject to full classification and authorization.
Expression
Product-specific composition of formula and object records
Statement
Status: DISABLED_ACTIVE_HOLD
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’SHIVA-CRYPTO’, class=’EXTERNAL_FINANCIAL_CANDIDATE’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product SHIVA-CRYPTO { purpose; formulas; families; evidence; permit; }
Literal
SHIVA-CRYPTO
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
EXTERNAL_FINANCIAL_CANDIDATE
Attribute
status=DISABLED_ACTIVE_HOLD
18.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
22


Chapter 19
Shiva Exchange Rule Reference - SHIVA-
EXCHANGE
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.SHIVA-EXCHANGE
Namespace
MJ.PBMEF.Product.SHIVA-EXCHANGE.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product SHIVA-EXCHANGE
Definition
Model transparent price-time, custody, audit, tax, and transfer rules without operating a market.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
SHIVA and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Model transparent price-time, custody, audit, tax, and transfer rules without operating a market.
Expression
Product-specific composition of formula and object records
Statement
Status: INTERNAL_SIMULATION_ONLY
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’SHIVA-EXCHANGE’, class=’MARKET_REFERENCE_MODEL’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product SHIVA-EXCHANGE { purpose; formulas; families; evidence; permit; }
Literal
SHIVA-EXCHANGE
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
MARKET_REFERENCE_MODEL
Attribute
status=INTERNAL_SIMULATION_ONLY
19.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
23


Chapter 20
Moana
Governed
Browser
-
MOANA-
BROWSER
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.MOANA-BROWSER
Namespace
MJ.PBMEF.Product.MOANA-BROWSER.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product MOANA-BROWSER
Definition
Present governed applications, evidence, holds, and uncertainty.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Present governed applications, evidence, holds, and uncertainty.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’MOANA-BROWSER’, class=’APPLICATION_PRODUCT’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product MOANA-BROWSER { purpose; formulas; families; evidence; permit; }
Literal
MOANA-BROWSER
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
APPLICATION_PRODUCT
Attribute
status=REFERENCE_CANDIDATE
20.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
24


Chapter 21
Aviator
Organizational
Workspace
-
AVIATOR-WORKSPACE
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.AVIATOR-WORKSPACE
Namespace
MJ.PBMEF.Product.AVIATOR-WORKSPACE.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product AVIATOR-WORKSPACE
Definition
Organize spaces, projects, decisions, knowledge, members, roles, and capabilities.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Organize spaces, projects, decisions, knowledge, members, roles, and capabilities.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’AVIATOR-WORKSPACE’, class=’APPLICATION_PRODUCT’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product AVIATOR-WORKSPACE { purpose; formulas; families; evidence; permit; }
Literal
AVIATOR-WORKSPACE
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
APPLICATION_PRODUCT
Attribute
status=REFERENCE_CANDIDATE
21.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
25


Chapter 22
Lecanto
Truthful
Visualization
-
LECANTO-VISUAL
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.LECANTO-VISUAL
Namespace
MJ.PBMEF.Product.LECANTO-VISUAL.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product LECANTO-VISUAL
Definition
Display system truth, provenance, topology, uncertainty, and evidence.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Display system truth, provenance, topology, uncertainty, and evidence.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’LECANTO-VISUAL’, class=’VISUAL_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product LECANTO-VISUAL { purpose; formulas; families; evidence; permit; }
Literal
LECANTO-VISUAL
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
VISUAL_SYSTEM
Attribute
status=REFERENCE_CANDIDATE
22.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
26


Chapter 23
Elsa Governed Marketplace Reference -
ELSA-MARKETPLACE
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.ELSA-MARKETPLACE
Namespace
MJ.PBMEF.Product.ELSA-MARKETPLACE.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product ELSA-MARKETPLACE
Definition
Coordinate semantic listings, workflow, accounting, execution, and resource evidence without live market authority.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Coordinate semantic listings, workflow, accounting, execution, and resource evidence without live market authority.
Expression
Product-specific composition of formula and object records
Statement
Status: INTERNAL_REFERENCE_ONLY
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’ELSA-MARKETPLACE’, class=’MARKETPLACE_REFERENCE’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product ELSA-MARKETPLACE { purpose; formulas; families; evidence; permit; }
Literal
ELSA-MARKETPLACE
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
MARKETPLACE_REFERENCE
Attribute
status=INTERNAL_REFERENCE_ONLY
23.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
27


Chapter 24
Shekina
Distributed
Continuity
-
SHEKINA-CONTINUITY
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.SHEKINA-CONTINUITY
Namespace
MJ.PBMEF.Product.SHEKINA-CONTINUITY.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product SHEKINA-CONTINUITY
Definition
Model bounded replicas, failover, continuity, and placement evidence.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Model bounded replicas, failover, continuity, and placement evidence.
Expression
Product-specific composition of formula and object records
Statement
Status: SPECIFICATION_CANDIDATE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’SHEKINA-CONTINUITY’, class=’INFRASTRUCTURE_REFERENCE’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product SHEKINA-CONTINUITY { purpose; formulas; families; evidence; permit; }
Literal
SHEKINA-CONTINUITY
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
INFRASTRUCTURE_REFERENCE
Attribute
status=SPECIFICATION_CANDIDATE
24.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
28


Chapter 25
Pearl
Hypothetical
Simulation
and
Information-Retention System - PEARL-
CONTAINMENT
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.PEARL-CONTAINMENT
Namespace
MJ.PBMEF.Product.PEARL-CONTAINMENT.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product PEARL-CONTAINMENT
Definition
Acquire, retain, replay, and compare variance simulations and transfer/regeneration opportunities without asserting physical containment.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Acquire, retain, replay, and compare variance simulations and transfer/regeneration opportunities without asserting physical containment.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_SIMULATION_ONLY_PHYSICAL_NOT_APPLICABLE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’PEARL-CONTAINMENT’, class=’HYPOTHETICAL_SIMULATION_AND_INFORMATION_RETENTION’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product PEARL-CONTAINMENT { purpose; formulas; families; evidence; permit; }
Literal
PEARL-CONTAINMENT
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
HYPOTHETICAL_SIMULATION_AND_INFORMATION_RETENTION
Attribute
status=REFERENCE_SIMULATION_ONLY_PHYSICAL_NOT_APPLICABLE
25.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
29


Chapter 26
Bangel
Spreadsheets
-
Bangel-
SPREADSHEETS
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.Bangel-SPREADSHEETS
Namespace
MJ.PBMEF.Product.Bangel-SPREADSHEETS.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product Bangel-SPREADSHEETS
Definition
Provide governed spreadsheet-like operational modeling through typed measurement cells, immutable revisions, Pearl simulation partitions, deterministic
recalculation, concurrency control, and audit evidence.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
Bangel and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Provide governed spreadsheet-like operational modeling through typed measurement cells, immutable revisions, Pearl simulation partitions, deterministic
recalculation, concurrency control, and audit evidence.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_MVP_PREPASSKEY
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’Bangel-SPREADSHEETS’, class=’MEASUREMENT_SPREADSHEET_PLATFORM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product Bangel-SPREADSHEETS { purpose; formulas; families; evidence; permit; }
Literal
Bangel-SPREADSHEETS
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
MEASUREMENT_SPREADSHEET_PLATFORM
Attribute
status=REFERENCE_MVP_PREPASSKEY
26.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
30


Chapter 27
JPOSMJ
Product
Portfolio
Envelope
-
JPOSMJ-PORTFOLIO
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.JPOSMJ-PORTFOLIO
Namespace
MJ.PBMEF.Product.JPOSMJ-PORTFOLIO.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product JPOSMJ-PORTFOLIO
Definition
Bind every JP-origin product candidate through MK physics representation, JO verification, participant evidence, and MJ bounded permit classification.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
JP and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Bind every JP-origin product candidate through MK physics representation, JO verification, participant evidence, and MJ bounded permit classification.
Expression
Product-specific composition of formula and object records
Statement
Status: PREPASSKEY_PORTFOLIO_ENVELOPE
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’JPOSMJ-PORTFOLIO’, class=’PRODUCT_FAMILY_ENVELOPE’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product JPOSMJ-PORTFOLIO { purpose; formulas; families; evidence; permit; }
Literal
JPOSMJ-PORTFOLIO
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
PRODUCT_FAMILY_ENVELOPE
Attribute
status=PREPASSKEY_PORTFOLIO_ENVELOPE
27.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
31


Chapter 28
MJ
Standard
Containment
Geometry
and Reference Gas Model - STANDARD-
CONTAINMENT-GEOMETRY
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.STANDARD-CONTAINMENT-GEOMETRY
Namespace
MJ.PBMEF.Product.STANDARD-CONTAINMENT-GEOMETRY.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product STANDARD-CONTAINMENT-GEOMETRY
Definition
Provide a scale-independent rectangle/cone/Sister/EVE/reservoir calculation standard and H2 reference-gas observation profile.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Provide a scale-independent rectangle/cone/Sister/EVE/reservoir calculation standard and H2 reference-gas observation profile.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_MVP_PHYSICAL_VALUES_HOLD
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’STANDARD-CONTAINMENT-GEOMETRY’, class=’PHYSICS_REFERENCE_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product STANDARD-CONTAINMENT-GEOMETRY { purpose; formulas; families; evidence; permit; }
Literal
STANDARD-CONTAINMENT-GEOMETRY
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
PHYSICS_REFERENCE_SYSTEM
Attribute
status=REFERENCE_MVP_PHYSICAL_VALUES_HOLD
28.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
32


Chapter 29
MJ Reservoir Collection,
Lake Buffer,
and
Spiral-Compatible
Re-entry
-
RESERVOIR-COLLECTION-MODULATION
Construct
Formula-specific expression
Module
MJ.PBMEF.Product.RESERVOIR-COLLECTION-MODULATION
Namespace
MJ.PBMEF.Product.RESERVOIR-COLLECTION-MODULATION.Day0
Import
Manifest, product register, applicable formulas, family and object definitions
Declaration
product RESERVOIR-COLLECTION-MODULATION
Definition
Model the rear reservoir loop, exterior outlet, lake-like buffer, circular inward/tangential re-entry, wave/friction references, adaptive sizing, and full Sis-
ter/EVE/Angel/M3/MK/JO/Mermaid/Shiva/MJ transaction path.
Capability
Reference, simulation, implementation candidate, or evidence lane according to status
Participant
MJ and applicable family manifestations
Relationship
JP origin -> MK physics -> JO proof -> family evidence -> M3 -> Mermaid/Shiva -> MJ
Function
Model the rear reservoir loop, exterior outlet, lake-like buffer, circular inward/tangential re-entry, wave/friction references, adaptive sizing, and full Sis-
ter/EVE/Angel/M3/MK/JO/Mermaid/Shiva/MJ transaction path.
Expression
Product-specific composition of formula and object records
Statement
Status: REFERENCE_MVP_PHYSICAL_VALUES_HOLD
Measurement
Product-specific; physical products require actual article and calibrated evidence
Constraint
No product inherits permission from portfolio membership or mathematical validity
Annotation
@product(id=’RESERVOIR-COLLECTION-MODULATION’, class=’PHYSICS_REFERENCE_SYSTEM’)
Directive
retain status, claims ceiling, evidence gates, and permit class
Block
product RESERVOIR-COLLECTION-MODULATION { purpose; formulas; families; evidence; permit; }
Literal
RESERVOIR-COLLECTION-MODULATION
Reference
manifest/PROJECT-PRODUCT-REGISTER.json and matching product white paper
Type
PHYSICS_REFERENCE_SYSTEM
Attribute
status=REFERENCE_MVP_PHYSICAL_VALUES_HOLD
29.1 Application and life-cycle potential
The product enters through a purpose-specific Bangel declaration. Elsa recovers its intended applica-
tion; JP composes its governed representation; MK determines physical applicability; JO verifies; the
appropriate family manifestations contribute evidence; M3 routes resources; Mermaid and Shiva pro-
cess balances or capital implications; MJ decides. A physical or external product remains held until its
own evidence and authority gates pass.
33


Chapter 30
Registered
white-paper
verification
crosswalk
34


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.1 MJ — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-01
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-01
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-01
Import
whitepapers/family/01-mj.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-01
Definition
Project root, founder-governed authority and final bounded permit decision. Project root, founder-governed authority and final bounded permit decision.
truth, measurement, human authority, stewardship, non-weaponization.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MJ
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-01’, path=’whitepapers/family/01-mj.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-01 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-01
Reference
whitepapers/family/01-mj.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.2 Bangel — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-02
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-02
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-02
Import
whitepapers/family/02-Bangel.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-02
Definition
Human-facing governed language that preserves purpose and command structure. Human-facing governed language that preserves purpose and command
structure. intent integrity, explicit types, traceability.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
Bangel
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-02’, path=’whitepapers/family/02-Bangel.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-02 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-02
Reference
whitepapers/family/02-Bangel.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 35 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.3 Elsa — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-03
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-03
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-03
Import
whitepapers/family/03-elsa.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-03
Definition
Deterministic semantic recovery and purpose-preservation layer. Deterministic semantic recovery and purpose-preservation layer. meaning fidelity, purpose
confinement, clarity.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
ELSA
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-03’, path=’whitepapers/family/03-elsa.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-03 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-03
Reference
whitepapers/family/03-elsa.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.4 JP — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-04
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-04
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-04
Import
whitepapers/family/04-jp.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-04
Definition
Canonical mathematical, algorithmic, topology, CAPO, and architecture representation. Canonical mathematical, algorithmic, topology, CAPO, and architec-
ture representation. mathematical rigor, provenance, equivalence.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
JP
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-04’, path=’whitepapers/family/04-jp.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-04 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-04
Reference
whitepapers/family/04-jp.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 36 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.5 Mika / MK — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-
WP-05
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-05
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-05
Import
whitepapers/family/05-mk.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-05
Definition
Physics Modulator System for dimensional, conservation, boundary, scale, and evidence representation. Physics Modulator System for dimensional, conser-
vation, boundary, scale, and evidence representation. physical truth, unit integrity, conservation, uncertainty honesty.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MK
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-05’, path=’whitepapers/family/05-mk.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-05 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-05
Reference
whitepapers/family/05-mk.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.6 JO — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-06
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-06
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-06
Import
whitepapers/family/06-jo.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-06
Definition
Deterministic type, unit, proof, validation, runtime, and evidence engine. Deterministic type, unit, proof, validation, runtime, and evidence engine. fail
closed, reproducibility, auditability.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
JO
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-06’, path=’whitepapers/family/06-jo.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-06 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-06
Reference
whitepapers/family/06-jo.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 37 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.7 MJOS — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-07
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-07
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-07
Import
whitepapers/family/07-mjos.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-07
Definition
Operating-system and infrastructure substrate inside MJ. Operating-system and infrastructure substrate inside MJ. bounded resources, continuity, isolation.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MJOS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-07’, path=’whitepapers/family/07-mjos.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-07 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-07
Reference
whitepapers/family/07-mjos.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.8 Angels — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-
08
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-08
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-08
Import
whitepapers/family/08-angels.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-08
Definition
Domain-specific observation, telemetry, hold, denial, and corrective-command family. Domain-specific observation, telemetry, hold, denial, and corrective-
command family. safety, watchfulness, correction.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
ANGELS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-08’, path=’whitepapers/family/08-angels.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-08 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-08
Reference
whitepapers/family/08-angels.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 38 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.9 Bellatrix — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-
09
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-09
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-09
Import
whitepapers/family/09-bellatrix.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-09
Definition
Independent defense, challenge, quarantine, hostile-deviation analysis, and denial. Independent defense, challenge, quarantine, hostile-deviation analysis,
and denial. defense, independence, containment.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
BELLATRIX
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-09’, path=’whitepapers/family/09-bellatrix.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-09 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-09
Reference
whitepapers/family/09-bellatrix.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.10 Sister — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-
10
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-10
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-10
Import
whitepapers/family/10-sister.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-10
Definition
Predictive digital twin, preallocation evidence, anomaly detection, and umbrella containment. Predictive digital twin, preallocation evidence, anomaly
detection, and umbrella containment. prediction, redundancy, early warning.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SISTER
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-10’, path=’whitepapers/family/10-sister.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-10 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-10
Reference
whitepapers/family/10-sister.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 39 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.11 EVE — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-11
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-11
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-11
Import
whitepapers/family/11-eve.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-11
Definition
Variance, evaporative effect, screen capture, leakage, smoke-like egress, and boundary-accounting evidence. Variance, evaporative effect, screen capture,
leakage, smoke-like egress, and boundary-accounting evidence. diligence, respect, loss accounting, boundary truth.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
EVE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-11’, path=’whitepapers/family/11-eve.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-11 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-11
Reference
whitepapers/family/11-eve.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.12 Mary / M3 — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-
WP-12
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-12
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-12
Import
whitepapers/family/12-m3.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-12
Definition
Bounded routing, API gateway, load balancing, connection pooling, and allocation stewardship. Bounded routing, API gateway, load balancing, connection
pooling, and allocation stewardship. fair allocation, resource hygiene, bounded routing.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
M3
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-12’, path=’whitepapers/family/12-m3.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-12 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-12
Reference
whitepapers/family/12-m3.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 40 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.13 Mermaid — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-
WP-13
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-13
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-13
Import
whitepapers/family/13-mermaid.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-13
Definition
Accounting, reconciliation, exposure, custody evidence, statements, tax lots, and financial consequence. Accounting, reconciliation, exposure, custody
evidence, statements, tax lots, and financial consequence. ledger truth, reconciliation, transparency.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MERMAID
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-13’, path=’whitepapers/family/13-mermaid.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-13 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-13
Reference
whitepapers/family/13-mermaid.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.14 Shiva — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-
14
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-14
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-14
Import
whitepapers/family/14-shiva.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-14
Definition
Finance, money, treasury, liquidity, capital-job classification, risk/opportunity analysis, and distribution proposal. Finance, money, treasury, liquidity, capital-
job classification, risk/opportunity analysis, and distribution proposal. liquidity first, stability, abundance with discipline, auditability.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SHIVA
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-14’, path=’whitepapers/family/14-shiva.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-14 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-14
Reference
whitepapers/family/14-shiva.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 41 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.15 Shekina — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-
WP-15
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-15
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-15
Import
whitepapers/family/15-shekina.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-15
Definition
Distributed placement, replication, continuity, and infrastructure evidence. Distributed placement, replication, continuity, and infrastructure evidence.
continuity, bounded placement, resilience.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SHEKINA
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-15’, path=’whitepapers/family/15-shekina.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-15 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-15
Reference
whitepapers/family/15-shekina.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.16 Belle — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-16
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-16
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-16
Import
whitepapers/family/16-belle.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-16
Definition
Engineering analysis, feasibility, topology review, and bounded proposals. Engineering analysis, feasibility, topology review, and bounded proposals. engi-
neering clarity, feasibility, benchmarking.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
BELLE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-16’, path=’whitepapers/family/16-belle.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-16 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-16
Reference
whitepapers/family/16-belle.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 42 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.17 Lecanto — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-
WP-17
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-17
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-17
Import
whitepapers/family/17-lecanto.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-17
Definition
Truthful governed visualization of state, provenance, uncertainty, and system structure. Truthful governed visualization of state, provenance, uncertainty,
and system structure. visibility, truth, uncertainty disclosure.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
LECANTO
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-17’, path=’whitepapers/family/17-lecanto.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-17 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-17
Reference
whitepapers/family/17-lecanto.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.18 Moana — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-
18
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-18
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-18
Import
whitepapers/family/18-moana.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-18
Definition
Browser and interaction presentation of governed applications and evidence. Browser and interaction presentation of governed applications and evidence.
interaction truth, accessibility, bounded presentation.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MOANA
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-18’, path=’whitepapers/family/18-moana.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-18 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-18
Reference
whitepapers/family/18-moana.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 43 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.19 Aviator — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-
19
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-19
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-19
Import
whitepapers/family/19-aviator.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-19
Definition
Organizational workspace, projects, decisions, roles, knowledge, and governed workflow. Organizational workspace, projects, decisions, roles, knowledge,
and governed workflow. understanding first, organization, decision trace.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
AVIATOR
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-19’, path=’whitepapers/family/19-aviator.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-19 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-19
Reference
whitepapers/family/19-aviator.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.20 CHI — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-20
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-20
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-20
Import
whitepapers/family/20-chi.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-20
Definition
Temporal variance and expected-observed-delivered-reconciled difference state. Temporal variance and expected-observed-delivered-reconciled difference
state. variance truth, time awareness.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
CHI
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-20’, path=’whitepapers/family/20-chi.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-20 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-20
Reference
whitepapers/family/20-chi.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 44 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.21 WATER — MJ Manifestation White Paper - MJ-PBMEF-FAMILY-WP-
21
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-FAMILY-WP-21
Namespace
MJ.PBMEF.Document.MJ-PBMEF-FAMILY-WP-21
Import
whitepapers/family/21-water.md
Declaration
whitepaper MJ-PBMEF-FAMILY-WP-21
Definition
Interval uncertainty, verified floor, and bounded unknown-state classification. Interval uncertainty, verified floor, and bounded unknown-state classification.
uncertainty honesty, bounded intervals.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
WATER
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-FAMILY-WP-21’, path=’whitepapers/family/21-water.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-FAMILY-WP-21 { source; hash; coverage; status; }
Literal
MJ-PBMEF-FAMILY-WP-21
Reference
whitepapers/family/21-water.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.22 MJ Physics Based Measurement Engineering Framework - MJ-
PBMEF-PRODUCT-WP-01
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-01
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-01
Import
whitepapers/products/01-pbmef-core.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-01
Definition
Integrate purpose, mathematics, physics, verification, safety, resource routing, accounting, finance, evidence, and bounded permit decisions. Integrate
purpose, mathematics, physics, verification, safety, resource routing, accounting, finance, evidence, and bounded permit decisions. measurement, safety,
traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
PBMEF-CORE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-01’, path=’whitepapers/products/01-pbmef-core.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-01 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-01
Reference
whitepapers/products/01-pbmef-core.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 45 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.23 Bangel Governed Measurement Language - MJ-PBMEF-PRODUCT-
WP-02
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-02
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-02
Import
whitepapers/products/02-Bangel-language.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-02
Definition
Express human purpose, typed measurements, formulas, evidence, and command pathways. Express human purpose, typed measurements, formulas,
evidence, and command pathways. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
Bangel-LANGUAGE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-02’, path=’whitepapers/products/02-Bangel-language.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-02 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-02
Reference
whitepapers/products/02-Bangel-language.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.24 Elsa Deterministic Semantic Recovery - MJ-PBMEF-PRODUCT-WP-
03
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-03
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-03
Import
whitepapers/products/03-elsa-semantics.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-03
Definition
Recover and preserve declared meaning without autonomous inference or authority. Recover and preserve declared meaning without autonomous inference
or authority. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
ELSA-SEMANTICS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-03’, path=’whitepapers/products/03-elsa-semantics.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-03 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-03
Reference
whitepapers/products/03-elsa-semantics.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 46 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.25 JP Mathematical and Architectural Canon - MJ-PBMEF-PRODUCT-
WP-04
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-04
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-04
Import
whitepapers/products/04-jp-canon.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-04
Definition
Represent equations, algorithms, CAPOs, topology, products, and proofs. Represent equations, algorithms, CAPOs, topology, products, and proofs. mea-
surement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
JP-CANON
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-04’, path=’whitepapers/products/04-jp-canon.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-04 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-04
Reference
whitepapers/products/04-jp-canon.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.26 Mika/MK Physics Modulator System - MJ-PBMEF-PRODUCT-WP-05
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-05
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-05
Import
whitepapers/products/05-mk-physics.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-05
Definition
Create physics representations and verify units, conservation, boundaries, scale, and evidence ceilings. Create physics representations and verify units,
conservation, boundaries, scale, and evidence ceilings. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MK-PHYSICS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-05’, path=’whitepapers/products/05-mk-physics.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-05 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-05
Reference
whitepapers/products/05-mk-physics.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 47 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.27 JO Deterministic Proof and Runtime - MJ-PBMEF-PRODUCT-WP-06
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-06
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-06
Import
whitepapers/products/06-jo-runtime.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-06
Definition
Verify types, units, authority, physics, tests, evidence, and bounded execution. Verify types, units, authority, physics, tests, evidence, and bounded execu-
tion. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
JO-RUNTIME
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-06’, path=’whitepapers/products/06-jo-runtime.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-06 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-06
Reference
whitepapers/products/06-jo-runtime.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.28 MJOS Operating Substrate - MJ-PBMEF-PRODUCT-WP-07
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-07
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-07
Import
whitepapers/products/07-mjos-substrate.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-07
Definition
Provide isolated resources, memory, storage, network, scheduling, and continuity under MJ leases. Provide isolated resources, memory, storage, network,
scheduling, and continuity under MJ leases. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MJOS-SUBSTRATE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-07’, path=’whitepapers/products/07-mjos-substrate.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-07 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-07
Reference
whitepapers/products/07-mjos-substrate.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 48 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.29 JP Semiconductor Phone Battery and OS Candidate - MJ-PBMEF-
PRODUCT-WP-08
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-08
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-08
Import
whitepapers/products/08-jp-sc-phone.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-08
Definition
Explore semiconductor-scale static intake, power wake, solar assist, battery, and operating-system integration. Explore semiconductor-scale static intake,
power wake, solar assist, battery, and operating-system integration. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
JP-SC-PHONE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-08’, path=’whitepapers/products/08-jp-sc-phone.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-08 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-08
Reference
whitepapers/products/08-jp-sc-phone.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.30 JP Large-Scale Boating Power Candidate - MJ-PBMEF-PRODUCT-
WP-09
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-09
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-09
Import
whitepapers/products/09-jp-ls-boat.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-09
Definition
Explore large-scale static intake, solar initiation, power bus, containment, and marine power integration. Explore large-scale static intake, solar initiation,
power bus, containment, and marine power integration. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
JP-LS-BOAT
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-09’, path=’whitepapers/products/09-jp-ls-boat.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-09 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-09
Reference
whitepapers/products/09-jp-ls-boat.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 49 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.31 JP Peaceful High-Energy Propulsion Research Candidate - MJ-
PBMEF-PRODUCT-WP-10
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-10
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-10
Import
whitepapers/products/10-jp-peaceful-propulsion.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-10
Definition
Explore peaceful propulsion measurement and control under non-weaponization, safety, and regulatory gates. Explore peaceful propulsion measurement
and control under non-weaponization, safety, and regulatory gates. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
JP-PEACEFUL-PROPULSION
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-10’, path=’whitepapers/products/10-jp-peaceful-propulsion.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-10 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-10
Reference
whitepapers/products/10-jp-peaceful-propulsion.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.32 Sister Predictive Containment System - MJ-PBMEF-PRODUCT-WP-
11
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-11
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-11
Import
whitepapers/products/11-sister-containment.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-11
Definition
Define a scale-independent physical-containment calculation pathway without claiming a realized physical article. This representation is governed inside MJ
and follows Bangel -> Elsa -> JP -> MK -> JO -> applicable evidence -> M3 -> Mermaid/Shiva -> MJ. Truthful measurement, scale independence, conserva-
tion, explicit uncertainty, and non-substitutable authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SISTER-CONTAINMENT
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-11’, path=’whitepapers/products/11-sister-containment.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-11 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-11
Reference
whitepapers/products/11-sister-containment.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 50 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.33 EVE
Variance
Screen
and
Egress
Accounting
-
MJ-PBMEF-
PRODUCT-WP-12
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-12
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-12
Import
whitepapers/products/12-eve-screen.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-12
Definition
Account for variance, evaporation, leakage, capture, and natural egress without silent loss. Account for variance, evaporation, leakage, capture, and natural
egress without silent loss. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
EVE-SCREEN
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-12’, path=’whitepapers/products/12-eve-screen.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-12 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-12
Reference
whitepapers/products/12-eve-screen.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.34 Angels Safety and Corrective Command System - MJ-PBMEF-
PRODUCT-WP-13
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-13
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-13
Import
whitepapers/products/13-angels-safety.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-13
Definition
Provide domain-bounded telemetry, hold, denial, isolation, and corrective protocols. Provide domain-bounded telemetry, hold, denial, isolation, and correc-
tive protocols. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
ANGELS-SAFETY
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-13’, path=’whitepapers/products/13-angels-safety.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-13 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-13
Reference
whitepapers/products/13-angels-safety.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 51 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.35 Mermaid Accounting and Reconciliation System - MJ-PBMEF-
PRODUCT-WP-14
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-14
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-14
Import
whitepapers/products/14-mermaid-recon.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-14
Definition
Maintain balances, custody evidence, exposure, tax lots, statements, and reconciliation. Maintain balances, custody evidence, exposure, tax lots, state-
ments, and reconciliation. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MERMAID-RECON
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-14’, path=’whitepapers/products/14-mermaid-recon.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-14 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-14
Reference
whitepapers/products/14-mermaid-recon.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.36 Shiva Dual Financial Rails - MJ-PBMEF-PRODUCT-WP-15
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-15
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-15
Import
whitepapers/products/15-shiva-rails.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-15
Definition
Separate stability/cash functions from investment and crypto risk while preserving liquidity-first ethics. Separate stability/cash functions from investment
and crypto risk while preserving liquidity-first ethics. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SHIVA-RAILS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-15’, path=’whitepapers/products/15-shiva-rails.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-15 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-15
Reference
whitepapers/products/15-shiva-rails.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 52 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.37 SHIVAS Internal Settlement Reflection - MJ-PBMEF-PRODUCT-WP-
16
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-16
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-16
Import
whitepapers/products/16-shivas-internal.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-16
Definition
Represent internal capital reflections without minting, redemption, public offer, or value guarantee. Represent internal capital reflections without minting,
redemption, public offer, or value guarantee. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SHIVAS-INTERNAL
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-16’, path=’whitepapers/products/16-shivas-internal.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-16 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-16
Reference
whitepapers/products/16-shivas-internal.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.38 Shiva Crypto External-Market Candidate - MJ-PBMEF-PRODUCT-
WP-17
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-17
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-17
Import
whitepapers/products/17-shiva-crypto.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-17
Definition
Model a separately governed external crypto rail subject to full classification and authorization. Model a separately governed external crypto rail subject to
full classification and authorization. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SHIVA-CRYPTO
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-17’, path=’whitepapers/products/17-shiva-crypto.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-17 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-17
Reference
whitepapers/products/17-shiva-crypto.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 53 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.39 Shiva Exchange Rule Reference - MJ-PBMEF-PRODUCT-WP-18
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-18
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-18
Import
whitepapers/products/18-shiva-exchange.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-18
Definition
Model transparent price-time, custody, audit, tax, and transfer rules without operating a market. Model transparent price-time, custody, audit, tax, and
transfer rules without operating a market. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SHIVA-EXCHANGE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-18’, path=’whitepapers/products/18-shiva-exchange.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-18 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-18
Reference
whitepapers/products/18-shiva-exchange.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.40 Moana Governed Browser - MJ-PBMEF-PRODUCT-WP-19
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-19
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-19
Import
whitepapers/products/19-moana-browser.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-19
Definition
Present governed applications, evidence, holds, and uncertainty. Present governed applications, evidence, holds, and uncertainty. measurement, safety,
traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MOANA-BROWSER
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-19’, path=’whitepapers/products/19-moana-browser.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-19 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-19
Reference
whitepapers/products/19-moana-browser.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 54 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.41 Aviator Organizational Workspace - MJ-PBMEF-PRODUCT-WP-20
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-20
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-20
Import
whitepapers/products/20-aviator-workspace.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-20
Definition
Organize spaces, projects, decisions, knowledge, members, roles, and capabilities. Organize spaces, projects, decisions, knowledge, members, roles, and
capabilities. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
AVIATOR-WORKSPACE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-20’, path=’whitepapers/products/20-aviator-workspace.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-20 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-20
Reference
whitepapers/products/20-aviator-workspace.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.42 Lecanto Truthful Visualization - MJ-PBMEF-PRODUCT-WP-21
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-21
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-21
Import
whitepapers/products/21-lecanto-visual.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-21
Definition
Display system truth, provenance, topology, uncertainty, and evidence. Display system truth, provenance, topology, uncertainty, and evidence. measure-
ment, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
LECANTO-VISUAL
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-21’, path=’whitepapers/products/21-lecanto-visual.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-21 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-21
Reference
whitepapers/products/21-lecanto-visual.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 55 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.43 Elsa Governed Marketplace Reference - MJ-PBMEF-PRODUCT-WP-
22
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-22
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-22
Import
whitepapers/products/22-elsa-marketplace.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-22
Definition
Coordinate semantic listings, workflow, accounting, execution, and resource evidence without live market authority. Coordinate semantic listings, workflow,
accounting, execution, and resource evidence without live market authority. measurement, safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
ELSA-MARKETPLACE
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-22’, path=’whitepapers/products/22-elsa-marketplace.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-22 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-22
Reference
whitepapers/products/22-elsa-marketplace.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.44 Shekina Distributed Continuity - MJ-PBMEF-PRODUCT-WP-23
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-23
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-23
Import
whitepapers/products/23-shekina-continuity.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-23
Definition
Model bounded replicas, failover, continuity, and placement evidence. Model bounded replicas, failover, continuity, and placement evidence. measurement,
safety, traceability, bounded development.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
SHEKINA-CONTINUITY
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-23’, path=’whitepapers/products/23-shekina-continuity.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-23 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-23
Reference
whitepapers/products/23-shekina-continuity.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 56 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.45 Pearl Hypothetical Simulation and Information-Retention Sys-
tem - MJ-PBMEF-PRODUCT-WP-24
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-24
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-24
Import
whitepapers/products/24-pearl-containment.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-24
Definition
Acquire, retain, compare, and replay variance information and simulation potential without asserting a physical Pearl container. This representation is
governed inside MJ and follows Bangel -> Elsa -> JP -> MK -> JO -> applicable evidence -> M3 -> Mermaid/Shiva -> MJ. Truthful measurement, scale
independence, conservation, explicit uncertainty, and non-substitutable authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
PEARL-CONTAINMENT
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-24’, path=’whitepapers/products/24-pearl-containment.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-24 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-24
Reference
whitepapers/products/24-pearl-containment.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.46 Bangel Spreadsheets - MJ-PBMEF-PRODUCT-WP-25
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-25
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-25
Import
whitepapers/products/25-Bangel-spreadsheets.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-25
Definition
Provide a physics-oriented, deterministic alternative to conventional spreadsheet workflows. Bangel Spreadsheets addresses founder-defined operational
risks: siloed files, conflicting versions, calculation bottlenecks, weak governance, and silent manual errors. Bangel Spreadsheets is an MJ product mani-
festation. A workbook is a governed measurement field. A cell is a typed object containing value, unit, uncertainty, formula, revision, lineage, authority,
evidence, and state. A workbook revision is immutable and content-addressed. Large workbooks are partitioned into Pearl simulation objects rather than
silently copied into disconnected files. Unified measurement meaning, immutable lineage, incremental work, low-latency correlation, typed units, explicit
uncertainty, concurrency safety, role-scoped access, auditability, and reality-based reporting.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
Bangel-SPREADSHEETS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-25’, path=’whitepapers/products/25-Bangel-spreadsheets.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-25 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-25
Reference
whitepapers/products/25-Bangel-spreadsheets.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 57 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.47 JPOSMJ Product Portfolio Envelope - MJ-PBMEF-PRODUCT-WP-26
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-26
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-26
Import
whitepapers/products/26-jposmj-portfolio.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-26
Definition
Give every JP-origin product and project option one consistent route through physics, proof, evidence, authority, and claims ceilings. ‘JPOSMJ‘ is an internal
portfolio label meaning JP product architecture →MK physics →JO verification →MJ permit classification. It is not a participant, authority, operating
system, or physical product. Consistent articulation, minimal revision, product comparability, physics completeness, evidence honesty, safety, and bounded
authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
JPOSMJ-PORTFOLIO
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-26’, path=’whitepapers/products/26-jposmj-portfolio.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-26 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-26
Reference
whitepapers/products/26-jposmj-portfolio.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.48 MJ Standard Containment Geometry and Reference Gas Model
- MJ-PBMEF-PRODUCT-WP-27
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-27
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-27
Import
whitepapers/products/27-standard-containment-geometry.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-27
Definition
Provide a scale-independent product-calculation standard for the founder-defined open rectangular intake, conical expansion, Sister umbrella capture,
isolated descent, EVE residual and escape accounting, bounded residual reservoir, and Pearl top-of-cone simulation anchor. The product is an MJ manifes-
tation. Bangel expresses the typed command; Elsa preserves its intended meaning; JP constructs the geometry and equation CAPOs; MK classifies physics
applicability and verifies dimensions, gas state, forces, conservation, uncertainty, and validity domain; JO verifies code and evidence; Sister, EVE, Angels,
Bellatrix, and M3 provide bounded routing, observation, containment, and safety evidence; Mermaid reconciles quantities; Shiva evaluates capital implica-
tions only when applicable; MJ retains the final bounded decision. Scale-independent ratios, explicit units, truthful evidence ceilings, co
Capability
Explain, constrain, cross-reference, and support founder review
Participant
STANDARD-CONTAINMENT-GEOMETRY
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-27’, path=’whitepapers/products/27-standard-containment-geometry.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-27 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-27
Reference
whitepapers/products/27-standard-containment-geometry.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 58 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.49 MJ Reservoir Collection Modulation and Return Loop - MJ-
PBMEF-PRODUCT-WP-28
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-PRODUCT-WP-28
Namespace
MJ.PBMEF.Document.MJ-PBMEF-PRODUCT-WP-28
Import
whitepapers/products/28-reservoir-collection-modulation.md
Declaration
whitepaper MJ-PBMEF-PRODUCT-WP-28
Definition
Provide one scale-independent reference product for the founder-defined backside outlet, outward-facing gap, connected but separately accounted
lake/buffer, circular inward-tangential re-entry, and continued variance-processing cycle. JP defines the geometry and transaction CAPOs; MK provides
physics applicability, units, flow, wave, force, friction, and conservation; JO produces deterministic proof and cycle receipts; Sister provides predictive
placement and physical-containment evidence; EVE records screen, pass-through, escape, evaporation, and residual state; Angels provide safety checks;
M3 routes every transaction under a bounded lease; Mermaid reconciles; Shiva analyzes opportunity only when capital applies; MJ alone decides whether a
bounded effect is eligible. Scale independence, small-discharge intent, actual-boundary truth, nonphysical Pearl-reference separation, control-volum
Capability
Explain, constrain, cross-reference, and support founder review
Participant
RESERVOIR-COLLECTION-MODULATION
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-PRODUCT-WP-28’, path=’whitepapers/products/28-reservoir-collection-modulation.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-PRODUCT-WP-28 { source; hash; coverage; status; }
Literal
MJ-PBMEF-PRODUCT-WP-28
Reference
whitepapers/products/28-reservoir-collection-modulation.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.50 R1 and R2 State Representation - MJ-PBMEF-REPRESENTATION-
WP-01
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-01
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-01
Import
whitepapers/representations/01-state-r1-r2.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-01
Definition
Define the minimum complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. Define the minimum
complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. truth, measurement, traceability, bounded
authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
STATE-R1-R2
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-01’, path=’whitepapers/representations/01-state-r1-r2.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-01 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-01
Reference
whitepapers/representations/01-state-r1-r2.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 59 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.51 Noise Floor and 23 mg Inflection - MJ-PBMEF-REPRESENTATION-
WP-02
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-02
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-02
Import
whitepapers/representations/02-noise-23mg.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-02
Definition
Separate the 23 mg pre-observational floor from the 24 mg containment-geometry reference and bind both to the first-noise plane. This representation
is governed inside MJ and follows Bangel -> Elsa -> JP -> MK -> JO -> applicable evidence -> M3 -> Mermaid/Shiva -> MJ. Truthful measurement, scale
independence, conservation, explicit uncertainty, and non-substitutable authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
NOISE-23MG
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-02’, path=’whitepapers/representations/02-noise-23mg.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-02 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-02
Reference
whitepapers/representations/02-noise-23mg.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.52 Upward 3x3 Node and Umbrella Representation - MJ-PBMEF-
REPRESENTATION-WP-03
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-03
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-03
Import
whitepapers/representations/03-node-3x3.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-03
Definition
Integrate the open rectangle and conical expansion with the normalized N1-N9, U/D/C, EVE, and reservoir topology. This representation is governed
inside MJ and follows Bangel -> Elsa -> JP -> MK -> JO -> applicable evidence -> M3 -> Mermaid/Shiva -> MJ. Truthful measurement, scale independence,
conservation, explicit uncertainty, and non-substitutable authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
NODE-3X3
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-03’, path=’whitepapers/representations/03-node-3x3.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-03 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-03
Reference
whitepapers/representations/03-node-3x3.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 60 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.53 Memory, Request Occultation, and Generational Handoff - MJ-
PBMEF-REPRESENTATION-WP-04
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-04
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-04
Import
whitepapers/representations/04-memory-handoff.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-04
Definition
Define the minimum complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. Define the minimum
complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. truth, measurement, traceability, bounded
authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
MEMORY-HANDOFF
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-04’, path=’whitepapers/representations/04-memory-handoff.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-04 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-04
Reference
whitepapers/representations/04-memory-handoff.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.54 Static Intake and Energy-Wake Representation - MJ-PBMEF-
REPRESENTATION-WP-05
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-05
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-05
Import
whitepapers/representations/05-static-impetus.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-05
Definition
Define the minimum complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. Define the minimum
complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. truth, measurement, traceability, bounded
authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
STATIC-IMPETUS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-05’, path=’whitepapers/representations/05-static-impetus.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-05 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-05
Reference
whitepapers/representations/05-static-impetus.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 61 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.55 EVE Variance, Screen, Evaporation, and Egress - MJ-PBMEF-
REPRESENTATION-WP-06
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-06
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-06
Import
whitepapers/representations/06-eve-egress.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-06
Definition
Define the minimum complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. Define the minimum
complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. truth, measurement, traceability, bounded
authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
EVE-EGRESS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-06’, path=’whitepapers/representations/06-eve-egress.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-06 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-06
Reference
whitepapers/representations/06-eve-egress.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.56 Shiva and Mermaid Financial Rails - MJ-PBMEF-REPRESENTATION-
WP-07
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-07
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-07
Import
whitepapers/representations/07-financial-rails.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-07
Definition
Define the minimum complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. Define the minimum
complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. truth, measurement, traceability, bounded
authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
FINANCIAL-RAILS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-07’, path=’whitepapers/representations/07-financial-rails.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-07 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-07
Reference
whitepapers/representations/07-financial-rails.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 62 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.57 Passkey, Claims Ceiling, and Repository Authentication - MJ-
PBMEF-REPRESENTATION-WP-08
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-08
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-08
Import
whitepapers/representations/08-passkey.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-08
Definition
Define the minimum complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. Define the minimum
complete logic, equations, authority boundaries, evidence states, and passkey claims for this representation. truth, measurement, traceability, bounded
authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
PASSKEY
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-08’, path=’whitepapers/representations/08-passkey.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-08 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-08
Reference
whitepapers/representations/08-passkey.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.58 Pearl Hypothetical Geometry and Acoustic Simulation Repre-
sentation - MJ-PBMEF-REPRESENTATION-WP-09
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-09
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-09
Import
whitepapers/representations/09-pearl-container-acoustics.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-09
Definition
Bind Pearl simulation to the top-of-cone observation plane and retain acoustic variables as simulation-only. This representation is governed inside MJ and
follows Bangel -> Elsa -> JP -> MK -> JO -> applicable evidence -> M3 -> Mermaid/Shiva -> MJ. Truthful measurement, scale independence, conservation,
explicit uncertainty, and non-substitutable authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
PEARL-CONTAINER-ACOUSTICS
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-09’, path=’whitepapers/representations/09-pearl-container-acoustics.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-09 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-09
Reference
whitepapers/representations/09-pearl-container-acoustics.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 63 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.59 Bangel Spreadsheets Cell, Dependency, Revision, and Pearl
Simulation Field - MJ-PBMEF-REPRESENTATION-WP-10
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-10
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-10
Import
whitepapers/representations/10-Bangel-spreadsheets-field.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-10
Definition
Define a spreadsheet-like operational field in which cells are typed measurement objects and workbook changes are immutable, auditable, incremental,
and partitionable. This representation is the technical core of Bangel Spreadsheets. It supports inventory, finance, project tracking, reporting, or other
processes only after the process, users, workload, service level, and authority are declared. Meaning consistency, version truth, low-latency recalculation,
role-scoped governance, manual-error resistance, complete audit, and measured capacity.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
Bangel-SPREADSHEETS-FIELD
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-10’, path=’whitepapers/representations/10-Bangel-spreadsheets-field.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-10 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-10
Reference
whitepapers/representations/10-Bangel-spreadsheets-field.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
30.60 Standard Containment Geometry and H2 Reference Represen-
tation - MJ-PBMEF-REPRESENTATION-WP-11
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-11
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-11
Import
whitepapers/representations/11-standard-containment-geometry-h2-reference.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-11
Definition
Provide one scale-independent containment calculation system for the open rectangle, conical expansion, Sister umbrella/descent/containment, EVE ac-
counting, residual reservoir, and Pearl cone-top simulation anchor. This representation connects JP geometry and formulas to MK physics, JO verification,
Sister and EVE evidence, M3 routing, Mermaid reconciliation, Shiva opportunity analysis when applicable, and MJ bounded decisions. Scale independence,
unit integrity, conservation, explicit gas state, truthful acceleration limits, and adaptive modification without rewriting core logic.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
STANDARD-CONTAINMENT-GEOMETRY-H2
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-11’, path=’whitepapers/representations/11-standard-containment-geometry-h2-reference.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-11 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-11
Reference
whitepapers/representations/11-standard-containment-geometry-h2-reference.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 64 of 65


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper VI - Products / White Papers
30.61 Reservoir Return Loop Physics Representation - MJ-PBMEF-
REPRESENTATION-WP-12
Construct
Formula-specific expression
Module
MJ.PBMEF.WhitePaper.MJ-PBMEF-REPRESENTATION-WP-12
Namespace
MJ.PBMEF.Document.MJ-PBMEF-REPRESENTATION-WP-12
Import
whitepapers/representations/12-reservoir-return-loop.md
Declaration
whitepaper MJ-PBMEF-REPRESENTATION-WP-12
Definition
Represent the outlet, buffer/lake, circular re-entry, perspective, wave-state, capacity, and transaction-cycle evidence of ‘RESERVOIR-COLLECTION-
MODULATION‘ without treating the Pearl simulation circle as a physical wall. The representation passes from Bangel and Elsa into JP geometry CAPOs,
MK physics checks, JO proof receipts, Sister/EVE/Angel evidence, M3 routing, Mermaid reconciliation, Shiva analysis when capital applies, and MJ bounded
decision. Typed state, explicit units, actual-boundary truth, uncertainty-aware clearance, separate control volumes, vector capacity, no same-cycle feed-
back, conservation, and non-substitutable authority.
Capability
Explain, constrain, cross-reference, and support founder review
Participant
RESERVOIR-RETURN-LOOP
Relationship
Source documentation -> manifest coverage -> passkey documentation manifest
Function
Provide rationale, formula links, scope, status, evidence ceiling, and boundaries
Expression
Narrative and referenced formulas
Statement
Documentation does not self-verify or self-authorize
Measurement
Not applicable unless the paper cites admitted measurement receipts
Constraint
Must match source hash, status, and claims ceiling
Annotation
@whitepaper(id=’MJ-PBMEF-REPRESENTATION-WP-12’, path=’whitepapers/representations/12-reservoir-return-loop.md’)
Directive
include or exclude with explicit manifest reason
Block
document MJ-PBMEF-REPRESENTATION-WP-12 { source; hash; coverage; status; }
Literal
MJ-PBMEF-REPRESENTATION-WP-12
Reference
whitepapers/representations/12-reservoir-return-loop.md
Type
WHITE_PAPER
Attribute
official_pre_day0_source=true
Page 65 of 65

Publication is pending owner review. White papers are excluded.