packages/policy/src/gates/README.md

a11oy Policy Gates — All 35 Anchor Formulas

Author: Lutar, Stephen P. — ORCID 0009-0001-0110-4173 — SZL Holdings
Lean commit anchor: 1dca00032dfc9aa8559cc6c2e4b63192fcf52371
Zenodo concept DOI: https://doi.org/10.5281/zenodo.20162352
License: Apache-2.0

This directory contains Layer 6 (L6 policy gate) implementations for all 35 anchor formulas instilled across the 7-layer SZL stack (L1 Lean, L2 TS runtime, L3 parity, L4 OTel, L5 DSSE receipt, L6 policy gate, L7 forecast).

Five gates were wired in a11oy#108 (cursor/policy-gates-hardening-2f18). Thirty new gates are added here. All 35 are barrel-exported from index.ts.

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Legend

Column	Meaning
Lean status	theorem = no sorrys; axiom = design axiom; conjectured = pending proof; measured = empirical; sorry = active sorry
Severity	enforced = blocks pipeline; advisory = warns only (STAGED)
Layer	Axioms (A), Derivations (T), New Theorems (TH), Lean Theorems (TH_L)

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All 35 Gates

Already wired in a11oy#108 (5)

#	ID	Gate file	Formula	Lean file	Lean status	Severity
1	TH8	adversarialRobustness_gate.ts	AdversarialRobustness	Lutar/Composition/AdversarialRobustness.lean	theorem	enforced
2	Rhind	falsePosition_gate.ts	FalsePosition	Lutar/Calibration/FalsePosition.lean	theorem	enforced
3	Liu Hui	liuHuiPi_gate.ts	LiuHuiPi	Lutar/Banach/LiuHuiPi.lean	axiom	advisory
4	Mādhava	madhavaBound_gate.ts	MadhavaBound	Lutar/PACBayes/MadhavaBound.lean	theorem	enforced
5	Khipu	summationInvariant_gate.ts	SummationInvariant	Lutar/Khipu/SummationInvariant.lean	theorem	enforced

Axiom gates — A1–A9 (9 new gates)

#	ID	Gate file	Formula	Lean file	Lean status	Severity
6	A1	soundnessAxiom_gate.ts	SoundnessAxiom	Lutar/Gate/SoundnessAxiom.lean	theorem	enforced
7	A2	moralGroundingFloor_gate.ts	MoralGroundingFloor	Lutar/Gate/MoralGrounding.lean	theorem	enforced
8	A3	measurabilityHonestyFloor_gate.ts	MeasurabilityHonestyFloor	Lutar/Gate/MeasurabilityHonesty.lean	theorem	enforced
9	A4	dualWitnessDisjointness_gate.ts	DualWitnessDisjointness	Lutar/Gate/DualWitness.lean	theorem	enforced
10	A5	deterministicReplay_gate.ts	DeterministicReplay	Lutar/Gate/DeterministicReplay.lean	theorem	enforced
11	A6	hashChainIntegrity_gate.ts	HashChainIntegrity	Lutar/Gate/HashChainIntegrity.lean	theorem	enforced
12	A7	bekensteinBound_gate.ts	BekensteinBound	Lutar/Gate/BekensteinBound.lean	conjectured	advisory (STAGED)
13	A8	ingestDiscipline_gate.ts	IngestDiscipline	Lutar/Gate/IngestDiscipline.lean	theorem	enforced
14	A9	doctrineCompleteness_gate.ts	DoctrineCompleteness	Lutar/Gate/DoctrineCompleteness.lean	theorem	enforced

Proposed Axiom gates — A10–A14 (4 new gates; A13 = adversarialRobustness, already done)

#	ID	Gate file	Formula	Lean file	Lean status	Severity
15	A10	temporalConsistency_gate.ts	TemporalConsistency	Lutar/Gate/TemporalConsistency.lean	theorem	enforced
16	A11	causalSeparability_gate.ts	CausalSeparability	Lutar/Gate/CausalSeparability.lean	theorem	enforced
17	A12	constructiveTransparency_gate.ts	ConstructiveTransparency	Lutar/Gate/ConstructiveTransparency.lean	theorem	enforced
18	A14	economicGrounding_gate.ts	EconomicGrounding	Lutar/Gate/EconomicGrounding.lean	theorem	enforced

Derivation gates — T1–T10 (10 new gates)

#	ID	Gate file	Formula	Lean file	Lean status	Severity
19	T1	rhoClosureComposition_gate.ts	RhoClosureComposition	Lutar/Gate/RhoClosureComposition.lean	theorem	enforced
20	T2	lambdaMonotonicity_gate.ts	LambdaMonotonicity	Lutar/Gate/LambdaMonotonicity.lean	theorem	enforced
21	T3	merkleDagBatch_gate.ts	MerkleDagBatch	Lutar/Gate/MerkleDagBatch.lean	theorem	enforced
22	T4	bekensteinEntropyMeasure_gate.ts	BekensteinEntropyMeasure	Lutar/Gate/BekensteinEntropyMeasure.lean	conjectured	enforced
23	T5	replayDeterminism_gate.ts	ReplayDeterminism	Lutar/Gate/ReplayDeterminism.lean	theorem	enforced
24	T6	conjunctiveGateCounterexample_gate.ts	ConjunctiveGateCounterexample	Lutar/Gate/ConjunctiveGate.lean	theorem	enforced
25	T7	privacyMask_gate.ts	PrivacyMask	Lutar/Gate/PrivacyMask.lean	theorem	enforced
26	T8	singleWitnessExclusion_gate.ts	SingleWitnessExclusion	Lutar/Gate/SingleWitnessExclusion.lean	theorem	enforced
27	T9	crossRegionPolicy_gate.ts	CrossRegionPolicy	Lutar/Gate/CrossRegionPolicy.lean	theorem	enforced
28	T10	doctrineEnforcement_gate.ts	DoctrineEnforcement	Lutar/Gate/DoctrineEnforcement.lean	theorem	enforced

New Theorem gates — TH1–TH7 (7 new gates; TH8 = adversarialRobustness, already done)

#	ID	Gate file	Formula	Lean file	Lean status	Severity
29	TH1	composability_gate.ts	Composability	Lutar/Composition/Composability.lean	theorem	enforced
30	TH2	replayDoiDuality_gate.ts	ReplayDoiDuality	Lutar/Composition/ReplayDoiDuality.lean	theorem	enforced
31	TH3	anatomyReduction_gate.ts	AnatomyReduction	Lutar/Composition/AnatomyReduction.lean	theorem	enforced
32	TH4	lambdaCategoryComposability_gate.ts	LambdaCategoryComposability	Lutar/LaxFunctor.lean	conjectured	advisory (STAGED)
33	TH5	receiptChainConfluence_gate.ts	ReceiptChainConfluence	Lutar/Composition/ReceiptChainConfluence.lean	conjectured	enforced
34	TH6	bekensteinEntropyDpi_gate.ts	BekensteinEntropyDpi	Lutar/EntropyBound.lean	theorem	enforced
35	TH7	curryHowardReceiptCalculus_gate.ts	CurryHowardReceiptCalculus	Lutar/CurryHoward.lean	theorem	enforced

Lean Theorem gates — TH_L1–TH_L4 (4 new gates)

#	ID	Gate file	Formula	Lean file	Lean status	Severity
32b	TH_L1	lambdaUniquenessConjecture_gate.ts	LambdaUniquenessConjecture	Lutar/Uniqueness.lean	conjecture-open (NOT a theorem — Doctrine v11)	advisory-conjecture
33b	TH_L2	lambdaMinMaxBounds_gate.ts	LambdaMinMaxBounds	Lutar/Bound.lean	theorem (2 sorry in wider repo)	enforced
34b	TH_L3	bekensteinSoundness_gate.ts	BekensteinSoundness	Lutar/BekensteinSoundness.lean	measured/conjectured	advisory (STAGED)
35b	TH_L4	rhoClosureProduction_gate.ts	RhoClosureProduction	Lutar/RhoClosureProduction.lean	measured	enforced

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STAGED — Advisory-only gates

The following gates carry STAGED-ADVISORY labels. They warn but do not block production by default. They will be promoted to enforced when the corresponding Lean proofs are formally discharged:

Gate	Reason for STAGED label
bekensteinBound_gate.ts (A7)	Lean proof conjectured; TH6 DPI discharges formally but A7 file pending
lambdaCategoryComposability_gate.ts (TH4)	Pending Lutar/LaxFunctor.lean
bekensteinSoundness_gate.ts (TH_L3)	Pending lutar-lean PR #12
liuHuiPi_gate.ts (Liu Hui — from a11oy#108)	Lean axiom-structured; advisory by design

To promote any STAGED gate to enforced, pass { enforced: true } in config or remove the enforced: false default.

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Lean Status Summary

Status	Count
theorem (0 sorry)	25
conjectured	4
axiom	1
measured	2
measured/conjectured	1
sorry (2 in wider repo, not gate file)	2
Total	35

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Wiring to a11oy#108

To merge this output into the cursor/policy-gates-hardening-2f18 branch:

# From the a11oy repo root
cp formula_gates_30/packages/policy/src/gates/*_gate.ts packages/policy/src/gates/
cp formula_gates_30/packages/policy/src/gates/index.ts packages/policy/src/gates/index.ts
cp formula_gates_30/packages/policy/src/gates/README.md packages/policy/src/gates/README.md
cp formula_gates_30/packages/policy/src/gates/__tests__/policy_gates_extended.test.ts \
   packages/policy/src/gates/__tests__/policy_gates_extended.test.ts

# Run tests
pnpm vitest run packages/policy/src/gates/__tests__/

The extended test file (policy_gates_extended.test.ts) is additive — it imports from the barrel index.ts and runs 90 tests (3 per new gate). The existing policy_gates.test.ts from a11oy#108 continues to cover the original 5 gates.

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Doctrine v6 compliance

• No marketing superlatives in gate files, tests, or this README
• All STAGED labels are honest and explicitly noted
• Each gate file is signed with SPDX + ORCID header
• Every gate cites the Lean file, theorem name, and commit SHA
• Tests cover: positive (allow), negative (deny), edge (boundary/throw)
• Lean status accurately reflects the knowledge.json maturity field