D011 / Pink / Review draft

PinkPaper Volume02 Formulas F001 F050

Terminology revised · evidence inherited

PinkPaper Volume02 Formulas F001 F050. Source pages 626-731. Nomenclature updated; historical equations, evidence limits and unresolved relationships retained.

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


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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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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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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)
}
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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.
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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)
}
98


PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper II - F001-F050
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)
}
100


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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}
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)
}
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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

Publication is pending owner review. White papers are excluded.