MJos Predictive Model | First manifestation of the Bangel Language
Terminology revised · evidence inherited
PinkPaper Volume03 Formulas F051 F100. Source pages 733-838. Nomenclature updated; historical equations, evidence limits and unresolved relationships retained.
MJ-PBMEF Pink Paper - Volume III
Formula Gateway Bindings F-051 through F-100
Michael Bangel - Author and Architect
August 2026
Contents
1
Verification method
5
2
F-051 - Pearl simulated regeneration vector
6
2.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3
F-052 - Pearl acoustic simulation wavelength
8
3.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
3.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
4
F-053 - Pearl acoustic simulation intensity
10
4.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
4.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
5
F-054 - Pearl acoustic simulation energy
12
5.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
5.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
6
F-055 - Pearl acoustic simulation observability gate
14
6.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
6.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
7
F-056 - Pearl acoustic simulation signal-to-noise
16
7.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
16
7.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
8
F-057 - Pearl acoustic simulation transfer function
18
8.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
8.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
9
F-058 - Pearl acoustic simulation setpoint
20
9.1 Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
9.2 Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
10F-059 - Bounded Pearl acoustic simulation adjustment
22
10.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
10.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
11F-060 - Pearl simulation registry reconciliation
24
11.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
24
11.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
12F-061 - Bangel Sheet cell state
26
12.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
12.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
13F-062 - Affected dependency closure
28
13.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
1
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
13.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
14F-063 - Incremental recompute cost
30
14.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
14.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
15F-064 - Concurrent edit arrival
32
15.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
15.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
16F-065 - Spreadsheet service utilization
34
16.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
16.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
17F-066 - Spreadsheet worker requirement
36
17.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
36
17.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
18F-067 - Recalculation latency
38
18.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
18.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
19F-068 - Spreadsheet data cost
40
19.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
19.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
20F-069 - Pearl simulation partition objective
42
20.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
20.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
21F-070 - Sheet revision root
44
21.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
21.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
22F-071 - Audit-particle completeness
46
22.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
46
22.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
23F-072 - Iterative recalculation stability
48
23.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
23.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
24F-073 - Revision conflict gate
50
24.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
24.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
25F-074 - Freshness age
52
25.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
25.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
26F-075 - Staleness gate
54
26.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
26.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
27F-076 - Data-performance correlation
56
27.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
27.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
28F-077 - Silo unification gate
58
28.1Gateway life-cycle example
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58
28.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
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29F-078 - Formula verification residual
60
29.1Gateway life-cycle example
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60
29.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
30F-079 - Operational intake completeness
62
30.1Gateway life-cycle example
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62
30.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
31F-080 - Spreadsheet capacity gate
64
31.1Gateway life-cycle example
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64
31.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
32F-081 - First-noise rectangle height
66
32.1Gateway life-cycle example
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66
32.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
33F-082 - Reference gas density
68
33.1Gateway life-cycle example
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68
33.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
34F-083 - 24 mg reference volume
70
34.1Gateway life-cycle example
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70
34.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
35F-084 - Rectangle depth
72
35.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
35.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
36F-085 - Cone height ratio
74
36.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
36.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
37F-086 - Cone top-width ratio
76
37.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
37.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
38F-087 - Cone area by height
78
38.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
38.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
39F-088 - Cone partial volume
80
39.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
39.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
40F-089 - Full conical-frustum volume
82
40.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
40.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
41F-090 - Pearl cone-top anchor
84
41.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
41.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
42F-091 - Observed gas mass
86
42.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
42.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
43F-092 - Gas mass-flow from height
88
43.1Gateway life-cycle example
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88
43.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
Page 3 of 105
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44F-093 - Observed gas-height predictor
90
44.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
44.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
91
45F-094 - Gas net-force balance
92
45.1Gateway life-cycle example
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92
45.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
46F-095 - Buoyancy force
94
46.1Gateway life-cycle example
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94
46.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
47F-096 - Drag force
96
47.1Gateway life-cycle example
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96
47.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
48F-097 - Flow continuity
98
48.1Gateway life-cycle example
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98
48.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
49F-098 - Residual reservoir capacity
100
49.1Gateway life-cycle example
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49.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
50F-099 - Umbrella/EVE/reservoir balance
102
50.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
50.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
51F-100 - Containment modification predicate
104
51.1Gateway life-cycle example
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
51.2Lifecycle from request to final output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Document control
Project
MJ: Physics Based Measurement Engineering Framework
Project ID
MJ-PBMEF-001
Source build
MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE
Document ID
MJ-PBMEF-PINK-PAPER-001/VOL-III
Author and architect
Michael Bangel
Status
FOUNDER_REVIEW_CANDIDATE_PENDING_FREEZE
Scope
Formula-level gateway bindings for F-051 through F-100.
Claims ceiling
This document is a private pre-Day-0 review and verification candidate. It authenticates no pri-
vate key and creates no physical validation, physical operation authority, product certification,
external regulatory authority, production deployment, financial-product launch, token issuance,
AI integration, or physical-coordinate approval. Formula pages distinguish mathematical validity,
reference implementation, simulation, measured evidence, authority, and execution.
Page 4 of 105
Chapter 1
Verification method
Each formula receives the same twenty-construct Bangel identity, a gateway-stage assignment, a life-
cycle example, and explicit evidence and ethics boundaries. The repetitive structure is intentional: it
allows formula-by-formula founder review and later automated completeness checking.
5
Chapter 2
F-051 - Pearl simulated regeneration
vector
Exact expression
G_P=[G_mass,G_energy,G_bytes,G_time,G_capital]
Meaning. Hypothetical opportunity vector; creates no physical or capital value.
Bound manifestations. EVE, MERMAID, SHIVA, MK, JO
Gateway stage. N1 prediction-first allocation, M3 routing, and G123 reconciliation
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_051
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MK
Declaration
formula F-051 ’Pearl simulated regeneration vector’
Definition
Hypothetical opportunity vector; creates no physical or capital value.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
EVE, MERMAID, SHIVA, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
N1 prediction-first allocation, M3 routing, and G123 reconciliation
Expression
G_P=[G_mass,G_energy,G_bytes,G_time,G_capital]
Statement
When typed inputs and evidence gates pass, evaluate F-051; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed vector; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-051’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-051); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-051 and applicable family/product/representation white papers
Type
typed vector
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’N1 prediction-first allocation, M3 routing, and G123 reconciliation’; physical_validation=false; author-
ity=false
2.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_051 : Formula<typed vector>
definition "Hypothetical opportunity vector; creates no physical or capital value."
expression `G_P=[G_mass,G_energy,G_bytes,G_time,G_capital]`
participants ["EVE", "MERMAID", "SHIVA", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
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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-051 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 7 of 105
Chapter 3
F-052 - Pearl acoustic simulation wave-
length
Exact expression
lambda_ac=c_medium/f_control
Meaning. Acoustic simulation variable under declared medium assumptions; no cohesion claim.
Bound manifestations. MK, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_052
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-052 ’Pearl acoustic simulation wavelength’
Definition
Acoustic simulation variable under declared medium assumptions; no cohesion claim.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
lambda_ac=c_medium/f_control
Statement
When typed inputs and evidence gates pass, evaluate F-052; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-052’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-052); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-052 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
3.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_052 : Formula<length>
definition "Acoustic simulation variable under declared medium assumptions; no cohesion
claim."
↪
expression `lambda_ac=c_medium/f_control`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
8
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Pink Paper III - F051-F100
3.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-052 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 9 of 105
Chapter 4
F-053 - Pearl acoustic simulation inten-
sity
Exact expression
I_ac=p_rms^2/(rho_medium*c_medium)
Meaning. Reference simulation intensity only; no physical actuation claim.
Bound manifestations. MK, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_053
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-053 ’Pearl acoustic simulation intensity’
Definition
Reference simulation intensity only; no physical actuation claim.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
I_ac=p_rms^2/(rho_medium*c_medium)
Statement
When typed inputs and evidence gates pass, evaluate F-053; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: power/area; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-053’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-053); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-053 and applicable family/product/representation white papers
Type
power/area
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
4.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_053 : Formula<power/area>
definition "Reference simulation intensity only; no physical actuation claim."
expression `I_ac=p_rms^2/(rho_medium*c_medium)`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
10
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
4.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-053 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 11 of 105
Chapter 5
F-054 - Pearl acoustic simulation energy
Exact expression
E_ac=integral(I_ac*A_effective)dt
Meaning. Hypothetical energy accounting for a future separately permitted experiment.
Bound manifestations. MK, EVE, MERMAID, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_054
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.JO
Declaration
formula F-054 ’Pearl acoustic simulation energy’
Definition
Hypothetical energy accounting for a future separately permitted experiment.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, MERMAID, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
E_ac=integral(I_ac*A_effective)dt
Statement
When typed inputs and evidence gates pass, evaluate F-054; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: energy; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-054’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-054); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-054 and applicable family/product/representation white papers
Type
energy
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
5.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_054 : Formula<energy>
definition "Hypothetical energy accounting for a future separately permitted experiment."
expression `E_ac=integral(I_ac*A_effective)dt`
participants ["MK", "EVE", "MERMAID", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
12
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
5.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-054 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 13 of 105
Chapter 6
F-055 - Pearl acoustic simulation ob-
servability gate
Exact expression
f_sample>=2*gamma*f_control AND f_control in calibrated_band AND SNR_f>=SNR_min
Meaning. Simulation input must be measurable to be accounted for; observability is not actuation.
Bound manifestations. MK, JO, ANGELS
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_055
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS
Declaration
formula F-055 ’Pearl acoustic simulation observability gate’
Definition
Simulation input must be measurable to be accounted for; observability is not actuation.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
MK, JO, ANGELS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
f_sample>=2*gamma*f_control AND f_control in calibrated_band AND SNR_f>=SNR_min
Statement
When typed inputs and evidence gates pass, evaluate F-055; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-055’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-055); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-055 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
6.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_055 : Formula<logical>
definition "Simulation input must be measurable to be accounted for; observability is not
actuation."
↪
expression `f_sample>=2*gamma*f_control AND f_control in calibrated_band AND
SNR_f>=SNR_min`
↪
participants ["MK", "JO", "ANGELS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
14
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Pink Paper III - F051-F100
}
6.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-055 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 15 of 105
Chapter 7
F-056 - Pearl acoustic simulation signal-
to-noise
Exact expression
SNR_f=P_signal(f)/P_noise(f)
Meaning. Simulation signal-to-noise ratio; advisory and non-authorizing.
Bound manifestations. MK, SISTER, EVE, JO
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_056
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-056 ’Pearl acoustic simulation signal-to-noise’
Definition
Simulation signal-to-noise ratio; advisory and non-authorizing.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, SISTER, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
SNR_f=P_signal(f)/P_noise(f)
Statement
When typed inputs and evidence gates pass, evaluate F-056; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-056’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-056); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-056 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
7.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_056 : Formula<ratio>
definition "Simulation signal-to-noise ratio; advisory and non-authorizing."
expression `SNR_f=P_signal(f)/P_noise(f)`
participants ["MK", "SISTER", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
16
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
7.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-056 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 17 of 105
Chapter 8
F-057 - Pearl acoustic simulation trans-
fer function
Exact expression
H_P(f)=Y_P(f)/U_P(f)
Meaning. Hypothetical or measured-later response mapping; no physical Pearl article exists.
Bound manifestations. MK, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_057
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-057 ’Pearl acoustic simulation transfer function’
Definition
Hypothetical or measured-later response mapping; no physical Pearl article exists.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
H_P(f)=Y_P(f)/U_P(f)
Statement
When typed inputs and evidence gates pass, evaluate F-057; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: output/input; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-057’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-057); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-057 and applicable family/product/representation white papers
Type
output/input
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
8.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_057 : Formula<output/input>
definition "Hypothetical or measured-later response mapping; no physical Pearl article
exists."
↪
expression `H_P(f)=Y_P(f)/U_P(f)`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
18
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
8.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-057 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 19 of 105
Chapter 9
F-058 - Pearl acoustic simulation set-
point
Exact expression
f*=argmin_{f in F_safe}(J_breach+lambda_E*E_ac+lambda_T*T_transfer)
Meaning. Simulation candidate only; no physical control setpoint.
Bound manifestations. MK, BELLE, JO, MJ
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_058
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.BELLE, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MJ
Declaration
formula F-058 ’Pearl acoustic simulation setpoint’
Definition
Simulation candidate only; no physical control setpoint.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, BELLE, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
f*=argmin_{f in F_safe}(J_breach+lambda_E*E_ac+lambda_T*T_transfer)
Statement
When typed inputs and evidence gates pass, evaluate F-058; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: frequency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-058’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-058); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-058 and applicable family/product/representation white papers
Type
frequency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
9.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_058 : Formula<frequency>
definition "Simulation candidate only; no physical control setpoint."
expression `f*=argmin_{f in F_safe}(J_breach+lambda_E*E_ac+lambda_T*T_transfer)`
participants ["MK", "BELLE", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
20
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
9.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-058 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 21 of 105
Chapter 10
F-059 - Bounded Pearl acoustic simula-
tion adjustment
Exact expression
f_next=clip((2/3)f+(1/3)f_target,f-df_max,f+df_max,f_min,f_max)
Meaning. One-third-damped simulation update only.
Bound manifestations. MK, JO, M3
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_059
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-059 ’Bounded Pearl acoustic simulation adjustment’
Definition
One-third-damped simulation update only.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
f_next=clip((2/3)f+(1/3)f_target,f-df_max,f+df_max,f_min,f_max)
Statement
When typed inputs and evidence gates pass, evaluate F-059; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: frequency; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-059’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-059); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2, 3, 1
Reference
pathways/FORMULA-REGISTER.json#F-059 and applicable family/product/representation white papers
Type
frequency
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
10.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_059 : Formula<frequency>
definition "One-third-damped simulation update only."
expression `f_next=clip((2/3)f+(1/3)f_target,f-df_max,f+df_max,f_min,f_max)`
participants ["MK", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
22
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
10.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-059 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 23 of 105
Chapter 11
F-060 - Pearl simulation registry recon-
ciliation
Exact expression
r_registry=N_allocated+N_received-N_transferred-N_closed-N_active
Meaning. Registry count reconciliation for simulation records, not physical containers.
Bound manifestations. MERMAID, SHIVA, M3, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference
Namespace
MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference.F_060
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.JO
Declaration
formula F-060 ’Pearl simulation registry reconciliation’
Definition
Registry count reconciliation for simulation records, not physical containers.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MERMAID, SHIVA, M3, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
r_registry=N_allocated+N_received-N_transferred-N_closed-N_active
Statement
When typed inputs and evidence gates pass, evaluate F-060; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: count; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-060’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-060); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-060 and applicable family/product/representation white papers
Type
count
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
11.1 Gateway life-cycle example
module MJ.PBMEF.pearl.hypothetical_simulation_acoustic_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_060 : Formula<count>
definition "Registry count reconciliation for simulation records, not physical containers."
expression `r_registry=N_allocated+N_received-N_transferred-N_closed-N_active`
participants ["MERMAID", "SHIVA", "M3", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
24
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
11.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-060 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 25 of 105
Chapter 12
F-061 - Bangel Sheet cell state
Exact expression
C_ij=<value,unit,uncertainty,formula,revision,lineage,authority,evidence>
Meaning. Every cell is a governed measurement object, not an untyped mutable value.
Bound manifestations. Bangel, JP, MK, JO
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_061
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-061 ’Bangel Sheet cell state’
Definition
Every cell is a governed measurement object, not an untyped mutable value.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
Bangel, JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
C_ij=<value,unit,uncertainty,formula,revision,lineage,authority,evidence>
Statement
When typed inputs and evidence gates pass, evaluate F-061; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed object; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-061’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-061); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-061 and applicable family/product/representation white papers
Type
typed object
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
12.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_061 : Formula<typed object>
definition "Every cell is a governed measurement object, not an untyped mutable value."
expression `C_ij=<value,unit,uncertainty,formula,revision,lineage,authority,evidence>`
participants ["Bangel", "JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
26
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
12.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-061 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 27 of 105
Chapter 13
F-062 - Affected dependency closure
Exact expression
A(U)=Reachable_G(U)
Meaning. Only cells reachable from changed cells are eligible for incremental recomputation.
Bound manifestations. JP, JO, M3
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_062
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-062 ’Affected dependency closure’
Definition
Only cells reachable from changed cells are eligible for incremental recomputation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
A(U)=Reachable_G(U)
Statement
When typed inputs and evidence gates pass, evaluate F-062; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: cell set; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-062’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-062); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-062 and applicable family/product/representation white papers
Type
cell set
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
13.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_062 : Formula<cell set>
definition "Only cells reachable from changed cells are eligible for incremental
recomputation."
↪
expression `A(U)=Reachable_G(U)`
participants ["JP", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
28
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
13.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-062 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 29 of 105
Chapter 14
F-063 - Incremental recompute cost
Exact expression
C_recalc=sum_{v in A}c_v+sum_{e in E(A)}t_e
Meaning. Measured compute and transfer work for an affected dependency closure.
Bound manifestations. MK, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_063
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-063 ’Incremental recompute cost’
Definition
Measured compute and transfer work for an affected dependency closure.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
C_recalc=sum_{v in A}c_v+sum_{e in E(A)}t_e
Statement
When typed inputs and evidence gates pass, evaluate F-063; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: work units; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-063’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-063); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-063 and applicable family/product/representation white papers
Type
work units
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
14.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_063 : Formula<work units>
definition "Measured compute and transfer work for an affected dependency closure."
expression `C_recalc=sum_{v in A}c_v+sum_{e in E(A)}t_e`
participants ["MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
30
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
14.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-063 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 31 of 105
Chapter 15
F-064 - Concurrent edit arrival
Exact expression
lambda_total=N_users*lambda_user
Meaning. Aggregate update arrival rate from measured concurrent-user activity.
Bound manifestations. JO, M3, MK
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_064
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK
Declaration
formula F-064 ’Concurrent edit arrival’
Definition
Aggregate update arrival rate from measured concurrent-user activity.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JO, M3, MK
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
lambda_total=N_users*lambda_user
Statement
When typed inputs and evidence gates pass, evaluate F-064; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: operations/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-064’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-064); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-064 and applicable family/product/representation white papers
Type
operations/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
15.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_064 : Formula<operations/time>
definition "Aggregate update arrival rate from measured concurrent-user activity."
expression `lambda_total=N_users*lambda_user`
participants ["JO", "M3", "MK"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
32
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
15.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-064 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 33 of 105
Chapter 16
F-065 - Spreadsheet service utilization
Exact expression
rho=lambda_total/(W*mu_worker)
Meaning. Capacity utilization for W deterministic workers.
Bound manifestations. JO, M3, MK
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_065
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MK
Declaration
formula F-065 ’Spreadsheet service utilization’
Definition
Capacity utilization for W deterministic workers.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, MK
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
rho=lambda_total/(W*mu_worker)
Statement
When typed inputs and evidence gates pass, evaluate F-065; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-065’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-065); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-065 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
16.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_065 : Formula<ratio>
definition "Capacity utilization for W deterministic workers."
expression `rho=lambda_total/(W*mu_worker)`
participants ["JO", "M3", "MK"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
34
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
16.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-065 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 35 of 105
Chapter 17
F-066 - Spreadsheet worker require-
ment
Exact expression
W_min=ceil(lambda_total/(rho_max*mu_worker))
Meaning. Minimum worker count for a precommitted utilization ceiling.
Bound manifestations. JO, M3, MJOS
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_066
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.MJOS
Declaration
formula F-066 ’Spreadsheet worker requirement’
Definition
Minimum worker count for a precommitted utilization ceiling.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, M3, MJOS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
W_min=ceil(lambda_total/(rho_max*mu_worker))
Statement
When typed inputs and evidence gates pass, evaluate F-066; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: count; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-066’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-066); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-066 and applicable family/product/representation white papers
Type
count
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
17.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_066 : Formula<count>
definition "Minimum worker count for a precommitted utilization ceiling."
expression `W_min=ceil(lambda_total/(rho_max*mu_worker))`
participants ["JO", "M3", "MJOS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
36
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
17.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-066 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 37 of 105
Chapter 18
F-067 - Recalculation latency
Exact expression
T_recalc=T_parse+T_dependency+max_p(T_partition,p)+T_commit
Meaning. End-to-end recalculation latency across logical Pearl simulation partitions.
Bound manifestations. MK, JO, M3
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_067
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3
Declaration
formula F-067 ’Recalculation latency’
Definition
End-to-end recalculation latency across logical Pearl simulation partitions.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, M3
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
T_recalc=T_parse+T_dependency+max_p(T_partition,p)+T_commit
Statement
When typed inputs and evidence gates pass, evaluate F-067; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-067’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-067); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-067 and applicable family/product/representation white papers
Type
time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
18.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_067 : Formula<time>
definition "End-to-end recalculation latency across logical Pearl simulation partitions."
expression `T_recalc=T_parse+T_dependency+max_p(T_partition,p)+T_commit`
participants ["MK", "JO", "M3"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
38
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
18.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-067 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 39 of 105
Chapter 19
F-068 - Spreadsheet data cost
Exact expression
C_data=B_store*c_store+B_transfer*c_transfer+t_cpu*c_cpu
Meaning. Storage, transfer, and compute cost remain separately evidenced before aggregation.
Bound manifestations. MERMAID, SHIVA, MK, JO
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_068
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MERMAID, MJ.PBMEF.Family.SHIVA, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-068 ’Spreadsheet data cost’
Definition
Storage, transfer, and compute cost remain separately evidenced before aggregation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MERMAID, SHIVA, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
C_data=B_store*c_store+B_transfer*c_transfer+t_cpu*c_cpu
Statement
When typed inputs and evidence gates pass, evaluate F-068; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: cost unit; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-068’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-068); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-068 and applicable family/product/representation white papers
Type
cost unit
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
19.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_068 : Formula<cost unit>
definition "Storage, transfer, and compute cost remain separately evidenced before
aggregation."
↪
expression `C_data=B_store*c_store+B_transfer*c_transfer+t_cpu*c_cpu`
participants ["MERMAID", "SHIVA", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
40
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
19.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-068 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 41 of 105
Chapter 20
F-069 - Pearl simulation partition objec-
tive
Exact expression
J_partition=alpha*max_p(L_p)+beta*sum_cut(w_e)+gamma*R_breach+delta*R_stale
Meaning. Logical partition objective with precommitted weights; breach term is simulation risk, not
physical containment.
Bound manifestations. JP, MK, JO, SISTER
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_069
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-069 ’Pearl simulation partition objective’
Definition
Logical partition objective with precommitted weights; breach term is simulation risk, not physical containment.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JP, MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
J_partition=alpha*max_p(L_p)+beta*sum_cut(w_e)+gamma*R_breach+delta*R_stale
Statement
When typed inputs and evidence gates pass, evaluate F-069; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: declared score; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-069’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-069); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-069 and applicable family/product/representation white papers
Type
declared score
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
20.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_069 : Formula<declared score>
definition "Logical partition objective with precommitted weights; breach term is
simulation risk, not physical containment."
↪
expression `J_partition=alpha*max_p(L_p)+beta*sum_cut(w_e)+gamma*R_breach+delta*R_stale`
participants ["JP", "MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
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}
20.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-069 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 43 of 105
Chapter 21
F-070 - Sheet revision root
Exact expression
H_rev=SHA256(parent_root||canonical_deltas||policy_epoch)
Meaning. Every committed change creates immutable content-addressed lineage.
Bound manifestations. Bangel, JP, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_070
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-070 ’Sheet revision root’
Definition
Every committed change creates immutable content-addressed lineage.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
Bangel, JP, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
H_rev=SHA256(parent_root||canonical_deltas||policy_epoch)
Statement
When typed inputs and evidence gates pass, evaluate F-070; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: digest; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-070’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-070); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
56
Reference
pathways/FORMULA-REGISTER.json#F-070 and applicable family/product/representation white papers
Type
digest
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
21.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_070 : Formula<digest>
definition "Every committed change creates immutable content-addressed lineage."
expression `H_rev=SHA256(parent_root||canonical_deltas||policy_epoch)`
participants ["Bangel", "JP", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
44
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21.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-070 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 45 of 105
Chapter 22
F-071 - Audit-particle completeness
Exact expression
AuditPass=AND(required_fields_present,receipts_valid)
Meaning. A critical spreadsheet command fails closed when its audit particle is incomplete.
Bound manifestations. JO, ANGELS, BELLATRIX, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_071
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.BELLATRIX, MJ.PBMEF.Family.MERMAID
Declaration
formula F-071 ’Audit-particle completeness’
Definition
A critical spreadsheet command fails closed when its audit particle is incomplete.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
JO, ANGELS, BELLATRIX, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
AuditPass=AND(required_fields_present,receipts_valid)
Statement
When typed inputs and evidence gates pass, evaluate F-071; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-071’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-071); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-071 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
22.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_071 : Formula<logical>
definition "A critical spreadsheet command fails closed when its audit particle is
incomplete."
↪
expression `AuditPass=AND(required_fields_present,receipts_valid)`
participants ["JO", "ANGELS", "BELLATRIX", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
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22.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-071 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 47 of 105
Chapter 23
F-072 - Iterative recalculation stability
Exact expression
spectral_radius(J_F)<1
Meaning. Declared iterative formulas require an evidenced locally stable fixed-point regime.
Bound manifestations. JP, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_072
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-072 ’Iterative recalculation stability’
Definition
Declared iterative formulas require an evidenced locally stable fixed-point regime.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
spectral_radius(J_F)<1
Statement
When typed inputs and evidence gates pass, evaluate F-072; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-072’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-072); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-072 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
23.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_072 : Formula<logical>
definition "Declared iterative formulas require an evidenced locally stable fixed-point
regime."
↪
expression `spectral_radius(J_F)<1`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
48
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23.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-072 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 49 of 105
Chapter 24
F-073 - Revision conflict gate
Exact expression
base_revision=head_revision OR valid_merge_receipt
Meaning. Stale writes cannot silently overwrite a newer revision.
Bound manifestations. Bangel, JO, ANGELS
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_073
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS
Declaration
formula F-073 ’Revision conflict gate’
Definition
Stale writes cannot silently overwrite a newer revision.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, JO, ANGELS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
base_revision=head_revision OR valid_merge_receipt
Statement
When typed inputs and evidence gates pass, evaluate F-073; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-073’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-073); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-073 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
24.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_073 : Formula<logical>
definition "Stale writes cannot silently overwrite a newer revision."
expression `base_revision=head_revision OR valid_merge_receipt`
participants ["Bangel", "JO", "ANGELS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
50
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Pink Paper III - F051-F100
24.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-073 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 51 of 105
Chapter 25
F-074 - Freshness age
Exact expression
Age=now-observed_at
Meaning. Age of a source observation or derived cell.
Bound manifestations. JO, MK, SISTER
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_074
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.SISTER
Declaration
formula F-074 ’Freshness age’
Definition
Age of a source observation or derived cell.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JO, MK, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
Age=now-observed_at
Statement
When typed inputs and evidence gates pass, evaluate F-074; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-074’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-074); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-074 and applicable family/product/representation white papers
Type
time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
25.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_074 : Formula<time>
definition "Age of a source observation or derived cell."
expression `Age=now-observed_at`
participants ["JO", "MK", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
52
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
25.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-074 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 53 of 105
Chapter 26
F-075 - Staleness gate
Exact expression
Age<=freshness_limit
Meaning. A cell is current only inside its declared freshness policy.
Bound manifestations. JO, ANGELS, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_075
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.ANGELS, MJ.PBMEF.Family.MERMAID
Declaration
formula F-075 ’Staleness gate’
Definition
A cell is current only inside its declared freshness policy.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
JO, ANGELS, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
Age<=freshness_limit
Statement
When typed inputs and evidence gates pass, evaluate F-075; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-075’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-075); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-075 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
26.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_075 : Formula<logical>
definition "A cell is current only inside its declared freshness policy."
expression `Age<=freshness_limit`
participants ["JO", "ANGELS", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
54
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26.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-075 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 55 of 105
Chapter 27
F-076 - Data-performance correlation
Exact expression
r_xy=Cov(X,Y)/(sigma_x*sigma_y)
Meaning. Descriptive correlation between data characteristics and performance; not a causal claim.
Bound manifestations. MK, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_076
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-076 ’Data-performance correlation’
Definition
Descriptive correlation between data characteristics and performance; not a causal claim.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r_xy=Cov(X,Y)/(sigma_x*sigma_y)
Statement
When typed inputs and evidence gates pass, evaluate F-076; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: ratio; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-076’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-076); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-076 and applicable family/product/representation white papers
Type
ratio
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
27.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_076 : Formula<ratio>
definition "Descriptive correlation between data characteristics and performance; not a
causal claim."
↪
expression `r_xy=Cov(X,Y)/(sigma_x*sigma_y)`
participants ["MK", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
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27.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-076 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 57 of 105
Chapter 28
F-077 - Silo unification gate
Exact expression
UnifiedMetric=SameMeaning AND SameUnit AND SamePeriod AND SameAuthority AND SameLineage
Meaning. Departmental sources unify only when semantic, unit, period, authority, and lineage condi-
tions agree.
Bound manifestations. ELSA, JP, JO, MERMAID
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_077
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.ELSA, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MERMAID
Declaration
formula F-077 ’Silo unification gate’
Definition
Departmental sources unify only when semantic, unit, period, authority, and lineage conditions agree.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
ELSA, JP, JO, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
UnifiedMetric=SameMeaning AND SameUnit AND SamePeriod AND SameAuthority AND SameLineage
Statement
When typed inputs and evidence gates pass, evaluate F-077; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-077’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-077); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-077 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
28.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_077 : Formula<logical>
definition "Departmental sources unify only when semantic, unit, period, authority, and
lineage conditions agree."
↪
expression `UnifiedMetric=SameMeaning AND SameUnit AND SamePeriod AND SameAuthority AND
SameLineage`
↪
participants ["ELSA", "JP", "JO", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
58
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28.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-077 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 59 of 105
Chapter 29
F-078 - Formula verification residual
Exact expression
r_formula=y_reported-y_recomputed
Meaning. Silent formula corruption is detected by independent deterministic recomputation.
Bound manifestations. JO, MK, ANGELS
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_078
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.ANGELS
Declaration
formula F-078 ’Formula verification residual’
Definition
Silent formula corruption is detected by independent deterministic recomputation.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
JO, MK, ANGELS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
r_formula=y_reported-y_recomputed
Statement
When typed inputs and evidence gates pass, evaluate F-078; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: output unit; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-078’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-078); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-078 and applicable family/product/representation white papers
Type
output unit
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
29.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_078 : Formula<output unit>
definition "Silent formula corruption is detected by independent deterministic
recomputation."
↪
expression `r_formula=y_reported-y_recomputed`
participants ["JO", "MK", "ANGELS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
60
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29.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-078 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 61 of 105
Chapter 30
F-079 - Operational intake complete-
ness
Exact expression
IntakePass=process_defined AND users_known AND workload_known AND SLA_known AND authority_known
Meaning. Scaling work begins only after the process, concurrency, workload, service target, and au-
thority are explicit.
Bound manifestations. Bangel, ELSA, JP, JO, MJ
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_079
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.ELSA, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.JO
Declaration
formula F-079 ’Operational intake completeness’
Definition
Scaling work begins only after the process, concurrency, workload, service target, and authority are explicit.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, ELSA, JP, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
IntakePass=process_defined AND users_known AND workload_known AND SLA_known AND authority_known
Statement
When typed inputs and evidence gates pass, evaluate F-079; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-079’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-079); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-079 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
30.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_079 : Formula<logical>
definition "Scaling work begins only after the process, concurrency, workload, service
target, and authority are explicit."
↪
expression `IntakePass=process_defined AND users_known AND workload_known AND SLA_known
AND authority_known`
↪
participants ["Bangel", "ELSA", "JP", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
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output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
30.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-079 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 63 of 105
Chapter 31
F-080 - Spreadsheet capacity gate
Exact expression
lambda_total<=rho_max*sum_p(mu_p) AND memory_required<=memory_available AND
cross_partition_edges<=cut_limit
↪
Meaning. Admission requires throughput, memory, and partition-boundary capacity to pass together.
Bound manifestations. MK, JO, M3, SISTER, MJOS
Gateway stage. Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Construct
Formula-specific expression
Module
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling
Namespace
MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling.F_080
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.M3, MJ.PBMEF.Family.SISTER
Declaration
formula F-080 ’Spreadsheet capacity gate’
Definition
Admission requires throughput, memory, and partition-boundary capacity to pass together.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
MK, JO, M3, SISTER, MJOS
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution
Expression
lambda_total<=rho_max*sum_p(mu_p) AND memory_required<=memory_available AND cross_partition_edges<=cut_limit
Statement
When typed inputs and evidence gates pass, evaluate F-080; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-080’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-080); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-080 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Bangel.begin workbook declaration, JP model, MK cost, JO deterministic execution’; physi-
cal_validation=false; authority=false
31.1 Gateway life-cycle example
module MJ.PBMEF.Bangel.spreadsheets.algorithms_scaling {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_080 : Formula<logical>
definition "Admission requires throughput, memory, and partition-boundary capacity to pass
together."
↪
expression `lambda_total<=rho_max*sum_p(mu_p) AND memory_required<=memory_available AND
cross_partition_edges<=cut_limit`
↪
participants ["MK", "JO", "M3", "SISTER", "MJOS"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
64
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31.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-080 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 65 of 105
Chapter 32
F-081 - First-noise rectangle height
Exact expression
H_R=h_noise,1
Meaning. Rectangle maximum height is the first validated noise-detection plane.
Bound manifestations. SISTER, MK, JO
Gateway stage. R1 prediction and normal-constellation calibration before N1
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_081
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-081 ’First-noise rectangle height’
Definition
Rectangle maximum height is the first validated noise-detection plane.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
R1 prediction and normal-constellation calibration before N1
Expression
H_R=h_noise,1
Statement
When typed inputs and evidence gates pass, evaluate F-081; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-081’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-081); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1
Reference
pathways/FORMULA-REGISTER.json#F-081 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’R1 prediction and normal-constellation calibration before N1’; physical_validation=false; authority=false
32.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_081 : Formula<length>
definition "Rectangle maximum height is the first validated noise-detection plane."
expression `H_R=h_noise,1`
participants ["SISTER", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
66
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
32.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-081 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 67 of 105
Chapter 33
F-082 - Reference gas density
Exact expression
rho_g=P*M/(Z*R*T)
Meaning. Actual gas density depends on measured pressure, temperature, molar mass, and compress-
ibility.
Bound manifestations. MK, JO, JP
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_082
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.JP
Declaration
formula F-082 ’Reference gas density’
Definition
Actual gas density depends on measured pressure, temperature, molar mass, and compressibility.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, JP
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
rho_g=P*M/(Z*R*T)
Statement
When typed inputs and evidence gates pass, evaluate F-082; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass/volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-082’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-082); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-082 and applicable family/product/representation white papers
Type
mass/volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
33.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_082 : Formula<mass/volume>
definition "Actual gas density depends on measured pressure, temperature, molar mass, and
compressibility."
↪
expression `rho_g=P*M/(Z*R*T)`
participants ["MK", "JO", "JP"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
68
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
33.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-082 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 69 of 105
Chapter 34
F-083 - 24 mg reference volume
Exact expression
V_24=m_24/rho_ref
Meaning. 24 mg defines a reference gas volume under a declared state and does not replace the 23 mg
floor.
Bound manifestations. JP, MK, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_083
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-083 ’24 mg reference volume’
Definition
24 mg defines a reference gas volume under a declared state and does not replace the 23 mg floor.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
V_24=m_24/rho_ref
Statement
When typed inputs and evidence gates pass, evaluate F-083; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-083’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-083); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
4
Reference
pathways/FORMULA-REGISTER.json#F-083 and applicable family/product/representation white papers
Type
volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
34.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_083 : Formula<volume>
definition "24 mg defines a reference gas volume under a declared state and does not
replace the 23 mg floor."
↪
expression `V_24=m_24/rho_ref`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
70
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
34.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-083 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 71 of 105
Chapter 35
F-084 - Rectangle depth
Exact expression
D_R=V_24/(W_R*H_R)
Meaning. Reference depth adapts to measured height and declared width.
Bound manifestations. SISTER, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_084
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-084 ’Rectangle depth’
Definition
Reference depth adapts to measured height and declared width.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
D_R=V_24/(W_R*H_R)
Statement
When typed inputs and evidence gates pass, evaluate F-084; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-084’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-084); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
4
Reference
pathways/FORMULA-REGISTER.json#F-084 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
35.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_084 : Formula<length>
definition "Reference depth adapts to measured height and declared width."
expression `D_R=V_24/(W_R*H_R)`
participants ["SISTER", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
72
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
35.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-084 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 73 of 105
Chapter 36
F-085 - Cone height ratio
Exact expression
H_C=k_H*H_R; k_H,std=2
Meaning. Standard cone height is twice rectangle height.
Bound manifestations. JP, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_085
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-085 ’Cone height ratio’
Definition
Standard cone height is twice rectangle height.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
H_C=k_H*H_R; k_H,std=2
Statement
When typed inputs and evidence gates pass, evaluate F-085; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-085’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-085); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-085 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
36.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_085 : Formula<length>
definition "Standard cone height is twice rectangle height."
expression `H_C=k_H*H_R; k_H,std=2`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
74
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
36.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-085 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 75 of 105
Chapter 37
F-086 - Cone top-width ratio
Exact expression
W_T=k_W*W_B; k_W,std=2
Meaning. Standard top characteristic width is twice bottom width.
Bound manifestations. JP, MK, JO
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_086
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-086 ’Cone top-width ratio’
Definition
Standard top characteristic width is twice bottom width.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
JP, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
W_T=k_W*W_B; k_W,std=2
Statement
When typed inputs and evidence gates pass, evaluate F-086; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-086’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-086); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
2
Reference
pathways/FORMULA-REGISTER.json#F-086 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
37.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_086 : Formula<length>
definition "Standard top characteristic width is twice bottom width."
expression `W_T=k_W*W_B; k_W,std=2`
participants ["JP", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
76
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
37.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-086 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 77 of 105
Chapter 38
F-087 - Cone area by height
Exact expression
A(z)=A_B*(1+(k_W-1)*z/H_C)^2
Meaning. Similar-section conical expansion area.
Bound manifestations. MK, JO, SISTER
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_087
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-087 ’Cone area by height’
Definition
Similar-section conical expansion area.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
A(z)=A_B*(1+(k_W-1)*z/H_C)^2
Statement
When typed inputs and evidence gates pass, evaluate F-087; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: area; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-087’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-087); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1, 2
Reference
pathways/FORMULA-REGISTER.json#F-087 and applicable family/product/representation white papers
Type
area
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
38.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_087 : Formula<area>
definition "Similar-section conical expansion area."
expression `A(z)=A_B*(1+(k_W-1)*z/H_C)^2`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
78
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
38.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-087 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 79 of 105
Chapter 39
F-088 - Cone partial volume
Exact expression
V_C(z)=A_B*(z+(k_W-1)z^2/H_C+(k_W-1)^2*z^3/(3H_C^2))
Meaning. Volume up to observed gas height.
Bound manifestations. MK, JO, SISTER
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_088
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-088 ’Cone partial volume’
Definition
Volume up to observed gas height.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
V_C(z)=A_B*(z+(k_W-1)z^2/H_C+(k_W-1)^2*z^3/(3H_C^2))
Statement
When typed inputs and evidence gates pass, evaluate F-088; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-088’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-088); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
1, 2, 3
Reference
pathways/FORMULA-REGISTER.json#F-088 and applicable family/product/representation white papers
Type
volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
39.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_088 : Formula<volume>
definition "Volume up to observed gas height."
expression `V_C(z)=A_B*(z+(k_W-1)z^2/H_C+(k_W-1)^2*z^3/(3H_C^2))`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
80
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
39.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-088 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 81 of 105
Chapter 40
F-089 - Full conical-frustum volume
Exact expression
V_C=H_C/3*(A_B+sqrt(A_B*A_T)+A_T)
Meaning. Full conical expansion volume.
Bound manifestations. MK, JO, JP
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_089
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.JP
Declaration
formula F-089 ’Full conical-frustum volume’
Definition
Full conical expansion volume.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, JP
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
V_C=H_C/3*(A_B+sqrt(A_B*A_T)+A_T)
Statement
When typed inputs and evidence gates pass, evaluate F-089; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-089’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-089); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
3
Reference
pathways/FORMULA-REGISTER.json#F-089 and applicable family/product/representation white papers
Type
volume
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
40.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_089 : Formula<volume>
definition "Full conical expansion volume."
expression `V_C=H_C/3*(A_B+sqrt(A_B*A_T)+A_T)`
participants ["MK", "JO", "JP"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
82
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
40.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-089 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 83 of 105
Chapter 41
F-090 - Pearl cone-top anchor
Exact expression
z_P0=H_R+H_C; standard=3H_R
Meaning. Pearl simulation begins at the top-of-cone information plane.
Bound manifestations. PEARL, MK, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_090
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.PEARL, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-090 ’Pearl cone-top anchor’
Definition
Pearl simulation begins at the top-of-cone information plane.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
PEARL, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
z_P0=H_R+H_C; standard=3H_R
Statement
When typed inputs and evidence gates pass, evaluate F-090; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-090’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-090); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
3
Reference
pathways/FORMULA-REGISTER.json#F-090 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
41.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_090 : Formula<length>
definition "Pearl simulation begins at the top-of-cone information plane."
expression `z_P0=H_R+H_C; standard=3H_R`
participants ["PEARL", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
84
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
41.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-090 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 85 of 105
Chapter 42
F-091 - Observed gas mass
Exact expression
m_g=rho_g*V_C(h_g)
Meaning. Gas mass from observed height and state-dependent density.
Bound manifestations. MK, EVE, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_091
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-091 ’Observed gas mass’
Definition
Gas mass from observed height and state-dependent density.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
m_g=rho_g*V_C(h_g)
Statement
When typed inputs and evidence gates pass, evaluate F-091; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-091’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-091); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-091 and applicable family/product/representation white papers
Type
mass
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
42.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_091 : Formula<mass>
definition "Gas mass from observed height and state-dependent density."
expression `m_g=rho_g*V_C(h_g)`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
86
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
42.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-091 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 87 of 105
Chapter 43
F-092 - Gas mass-flow from height
Exact expression
m_dot=rho*A(h_g)*h_dot_g+V_C(h_g)*rho_dot
Meaning. Mass-flow accounting includes density changes.
Bound manifestations. MK, EVE, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_092
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-092 ’Gas mass-flow from height’
Definition
Mass-flow accounting includes density changes.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
m_dot=rho*A(h_g)*h_dot_g+V_C(h_g)*rho_dot
Statement
When typed inputs and evidence gates pass, evaluate F-092; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: mass/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-092’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-092); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-092 and applicable family/product/representation white papers
Type
mass/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
43.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_092 : Formula<mass/time>
definition "Mass-flow accounting includes density changes."
expression `m_dot=rho*A(h_g)*h_dot_g+V_C(h_g)*rho_dot`
participants ["MK", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
88
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
43.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-092 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 89 of 105
Chapter 44
F-093 - Observed gas-height predictor
Exact expression
h_hat=clip(h+v*dt+0.5*a*dt^2,0,H_C)
Meaning. Bounded prediction of observed gas-front height.
Bound manifestations. SISTER, MK, JO
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_093
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-093 ’Observed gas-height predictor’
Definition
Bounded prediction of observed gas-front height.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
SISTER, MK, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
h_hat=clip(h+v*dt+0.5*a*dt^2,0,H_C)
Statement
When typed inputs and evidence gates pass, evaluate F-093; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: length; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-093’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-093); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.5, 2, 0
Reference
pathways/FORMULA-REGISTER.json#F-093 and applicable family/product/representation white papers
Type
length
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
44.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_093 : Formula<length>
definition "Bounded prediction of observed gas-front height."
expression `h_hat=clip(h+v*dt+0.5*a*dt^2,0,H_C)`
participants ["SISTER", "MK", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
90
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
44.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-093 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 91 of 105
Chapter 45
F-094 - Gas net-force balance
Exact expression
m_eff*a_z=F_b+F_p+F_act-F_d-F_wall-F_mix
Meaning. Geometry alone does not guarantee acceleration.
Bound manifestations. MK, JO, SISTER
Gateway stage. MJ.23 typed measurement branch and MK physics classification
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_094
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-094 ’Gas net-force balance’
Definition
Geometry alone does not guarantee acceleration.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
MJ.23 typed measurement branch and MK physics classification
Expression
m_eff*a_z=F_b+F_p+F_act-F_d-F_wall-F_mix
Statement
When typed inputs and evidence gates pass, evaluate F-094; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: force; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-094’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-094); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-094 and applicable family/product/representation white papers
Type
force
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’MJ.23 typed measurement branch and MK physics classification’; physical_validation=false; author-
ity=false
45.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_094 : Formula<force>
definition "Geometry alone does not guarantee acceleration."
expression `m_eff*a_z=F_b+F_p+F_act-F_d-F_wall-F_mix`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
92
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
45.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-094 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 93 of 105
Chapter 46
F-095 - Buoyancy force
Exact expression
F_b=(rho_ambient-rho_g)*g*V_g
Meaning. Reference buoyancy term under declared environment.
Bound manifestations. MK, JO, EVE
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_095
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE
Declaration
formula F-095 ’Buoyancy force’
Definition
Reference buoyancy term under declared environment.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, EVE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
F_b=(rho_ambient-rho_g)*g*V_g
Statement
When typed inputs and evidence gates pass, evaluate F-095; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: force; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-095’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-095); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-095 and applicable family/product/representation white papers
Type
force
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
46.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_095 : Formula<force>
definition "Reference buoyancy term under declared environment."
expression `F_b=(rho_ambient-rho_g)*g*V_g`
participants ["MK", "JO", "EVE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
94
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
46.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-095 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 95 of 105
Chapter 47
F-096 - Drag force
Exact expression
F_d=0.5*C_d*rho_ambient*A_projected*u*abs(u)
Meaning. Reference drag term under declared coefficient and flow.
Bound manifestations. MK, JO, EVE
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_096
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.EVE
Declaration
formula F-096 ’Drag force’
Definition
Reference drag term under declared coefficient and flow.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, EVE
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
F_d=0.5*C_d*rho_ambient*A_projected*u*abs(u)
Statement
When typed inputs and evidence gates pass, evaluate F-096; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: force; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-096’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-096); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0.5
Reference
pathways/FORMULA-REGISTER.json#F-096 and applicable family/product/representation white papers
Type
force
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
47.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_096 : Formula<force>
definition "Reference drag term under declared coefficient and flow."
expression `F_d=0.5*C_d*rho_ambient*A_projected*u*abs(u)`
participants ["MK", "JO", "EVE"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
96
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
47.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-096 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 97 of 105
Chapter 48
F-097 - Flow continuity
Exact expression
Q=A(z)*u(z)
Meaning. For fixed flow, increasing area does not itself accelerate the gas.
Bound manifestations. MK, JO, SISTER
Gateway stage. JP canonical representation, MK applicability, JO proof, and bounded MJ output
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_097
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO, MJ.PBMEF.Family.SISTER
Declaration
formula F-097 ’Flow continuity’
Definition
For fixed flow, increasing area does not itself accelerate the gas.
Capability
MEASURE_REFERENCE, SIMULATE, VERIFY_UNITS, RECONCILE
Participant
MK, JO, SISTER
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
JP canonical representation, MK applicability, JO proof, and bounded MJ output
Expression
Q=A(z)*u(z)
Statement
When typed inputs and evidence gates pass, evaluate F-097; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: volume/time; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-097’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-097); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-097 and applicable family/product/representation white papers
Type
volume/time
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’JP canonical representation, MK applicability, JO proof, and bounded MJ output’; physi-
cal_validation=false; authority=false
48.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_097 : Formula<volume/time>
definition "For fixed flow, increasing area does not itself accelerate the gas."
expression `Q=A(z)*u(z)`
participants ["MK", "JO", "SISTER"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
98
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
48.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-097 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 99 of 105
Chapter 49
F-098 - Residual reservoir capacity
Exact expression
C_res,k=gamma_k*C_rect,k; 0<=gamma_k<1
Meaning. Residual reservoir remains smaller than rectangle reference capacity.
Bound manifestations. SISTER, EVE, JO
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_098
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.JO
Declaration
formula F-098 ’Residual reservoir capacity’
Definition
Residual reservoir remains smaller than rectangle reference capacity.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
SISTER, EVE, JO
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
C_res,k=gamma_k*C_rect,k; 0<=gamma_k<1
Statement
When typed inputs and evidence gates pass, evaluate F-098; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed capacity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-098’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-098); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
0, 1
Reference
pathways/FORMULA-REGISTER.json#F-098 and applicable family/product/representation white papers
Type
typed capacity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
49.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_098 : Formula<typed capacity>
definition "Residual reservoir remains smaller than rectangle reference capacity."
expression `C_res,k=gamma_k*C_rect,k; 0<=gamma_k<1`
participants ["SISTER", "EVE", "JO"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
100
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
49.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-098 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 101 of 105
Chapter 50
F-099 - Umbrella/EVE/reservoir balance
Exact expression
q_cone=q_down+q_EVE+q_res+q_escape+r
Meaning.
Downward redistribution, EVE evidence, reservoir admission, and escape are separately
accounted.
Bound manifestations. EVE, SISTER, MERMAID
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_099
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.EVE, MJ.PBMEF.Family.SISTER, MJ.PBMEF.Family.MERMAID
Declaration
formula F-099 ’Umbrella/EVE/reservoir balance’
Definition
Downward redistribution, EVE evidence, reservoir admission, and escape are separately accounted.
Capability
REPRESENT, CALCULATE, VERIFY, RECEIPT
Participant
EVE, SISTER, MERMAID
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
q_cone=q_down+q_EVE+q_res+q_escape+r
Statement
When typed inputs and evidence gates pass, evaluate F-099; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: typed quantity; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-099’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-099); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-099 and applicable family/product/representation white papers
Type
typed quantity
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
50.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_099 : Formula<typed quantity>
definition "Downward redistribution, EVE evidence, reservoir admission, and escape are
separately accounted."
↪
expression `q_cone=q_down+q_EVE+q_res+q_escape+r`
participants ["EVE", "SISTER", "MERMAID"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
102
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
50.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-099 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 103 of 105
Chapter 51
F-100 - Containment modification pred-
icate
Exact expression
Valid(theta)=typed&positive&recomputed&conserved&bounded&evidenced&MK&JO&MJ
Meaning. Size changes preserve core logic but require full recalculation and gates.
Bound manifestations. Bangel, JP, MK, JO, MJ
Gateway stage. Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Construct
Formula-specific expression
Module
MJ.PBMEF.containment.geometry_h2_reference
Namespace
MJ.PBMEF.containment.geometry_h2_reference.F_100
Import
MJ.PBMEF.Manifest, MJ.PBMEF.Formulas, MJ.PBMEF.Family.Bangel, MJ.PBMEF.Family.JP, MJ.PBMEF.Family.MK, MJ.PBMEF.Family.JO
Declaration
formula F-100 ’Containment modification predicate’
Definition
Size changes preserve core logic but require full recalculation and gates.
Capability
CLASSIFY, VALIDATE, HOLD, DENY
Participant
Bangel, JP, MK, JO, MJ
Relationship
Human purpose -> MJ -> Bangel -> Elsa -> JP -> MK -> JO -> evidence families -> M3 -> Mermaid/Shiva -> MJ -> JO output
Function
Sister/EVE/MK/JO containment or simulation evidence before MJ permit
Expression
Valid(theta)=typed&positive&recomputed&conserved&bounded&evidenced&MK&JO&MJ
Statement
When typed inputs and evidence gates pass, evaluate F-100; otherwise preserve HOLD, FAIL_TECHNICAL, or DENY.
Measurement
Result dimension/type: logical; physical inputs require units, boundary, time, calibration, and uncertainty.
Constraint
UNKNOWN != 0; no self-authorization; no cross-unit coercion; evidence ceiling controls claims.
Annotation
@formula(id=’F-100’, source=’pathways/FORMULA-REGISTER.json’, build=’MJ-PBMEF-DAY0-R5-REVIEW-CANDIDATE’)
Directive
verify_with(JP,MK,JO); route_with(M3 when applicable); reconcile_with(Mermaid/Shiva when applicable); permit_by(MJ).
Block
R0 { Bangel.begin; R1.predict; JP.represent(F-100); MK.classify; JO.verify; N1.allocate_if_applicable; MJ.decide; JO.receipt; }
Literal
No numeric literal; symbolic inputs only
Reference
pathways/FORMULA-REGISTER.json#F-100 and applicable family/product/representation white papers
Type
logical
Attribute
status=REFERENCE_OR_TYPED_CANON; stage=’Sister/EVE/MK/JO containment or simulation evidence before MJ permit’; physical_validation=false;
authority=false
51.1 Gateway life-cycle example
module MJ.PBMEF.containment.geometry_h2_reference {
import MJ.PBMEF.Manifest
import MJ.PBMEF.Formulas
declaration F_100 : Formula<logical>
definition "Size changes preserve core logic but require full recalculation and gates."
expression `Valid(theta)=typed&positive&recomputed&conserved&bounded&evidenced&MK&JO&MJ`
participants ["Bangel", "JP", "MK", "JO", "MJ"]
constraint UNKNOWN != 0
constraint authority == MJ.only
directive JP.represent -> MK.classify -> JO.verify
directive N1.allocate when resource_path_applicable
directive M3.route when handoff_applicable
directive Mermaid.reconcile when balance_applicable
directive Shiva.analyze when capital_applicable
output JO.receipt(PASS | HOLD | FAIL_TECHNICAL | DENY)
}
104
PRIVATE PRE-DAY-0 - UNSIGNED REVIEW CANDIDATE
Pink Paper III - F051-F100
51.2 Lifecycle from request to final output
1. R/R0: receive founder or user purpose and exact command scope.
2. Bangel.begin: parse modules, namespaces, declarations, literals, types, constraints, and directives.
3. Elsa: recover semantic purpose, variable meaning, and ambiguity without creating authority.
4. JP: create the canonical CAPO for F-100 and its assumptions, inputs, outputs, and invariants.
5. MK: classify direct-physical, resource-physical, or abstract-nonphysical applicability; validate units,
boundary, conservation, scale, and evidence ceiling.
6. JO: run deterministic validation, preserve unknowns, and create a proof-receipt candidate.
7. R1: hold the object in unidentified transition until required evidence is sufficient.
8. N1: when allocation applies, use the prediction-first node and exact front-end allocation constraints;
no physical coordinate is inferred.
9. Angels/Bellatrix/Sister/EVE: provide applicable safety, anomaly, prediction, containment, screen, and
egress evidence.
10. M3: route admitted resources and handoffs without minting authority.
11. Mermaid/Shiva: reconcile balances and financial implications when relevant.
12. MJ: issue PASS, HOLD, FAIL_TECHNICAL, or DENY within the bounded permit class.
13. JO: execute only admitted non-prohibited effects and emit the final R2 living-static receipt.
Evidence and ethics boundary
Mathematical correctness does not prove physical performance and does not authorize an effect. A
formula may remain fully valid while a product instance is held for missing calibration, dimensions,
environmental state, uncertainty, authority, or safety evidence. Weaponized use, destructive de-
livery, offensive targeting, and authorization laundering are DENY states.
Page 105 of 105