SNAPKITTY-PROOFS

Copyright (c) 2026 Ahmad Ali Parr / SNAPKITTYWEST. All Rights Reserved. See LICENSE — Sovereign Source License v1.0. Forking does not grant usage rights.

Formal verification artifacts for the SnapKitty Sovereign OS. Three proof languages. One truth. Mathematically fingerprinted.

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Structure

proofs/
├── lean4/
│   ├── SovereignMorphism.lean      — MOC→Banach morphism (h_morphism, closes Ryan's sorry)
│   ├── SovereignFingerprint.lean   — Math traps: Fibonacci-Ahmad chain, Pisano-108 lock
│   ├── policy-kernel/              — Sovereign Policy Kernel (verdict algebra, policy DSL)
│   └── bifrost-policy/             — Bifrost event validity (JitCompile, CapTransfer, Attestation)
├── prolog/
│   ├── shrew_observer.pl           — SHREW: 4-level attestation witness (read-only)
│   ├── edaulc_verify.pl            — EDAULC: 5-pass ERE verification engine
│   └── quantum_monad.pl            — Quantum monad: Watchtowers, METATRON, 49th Call
└── haskell/
    ├── quantum_monad.hs            — Quantum superposition monad (Born-rule collapse)
    ├── no_cloning.hs               — No-Cloning Theorem (LinearTypes GADT v2.0)
    └── thermal.hs                  — Thermodynamic Window Engine (proven lo < hi)

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The Proof Stack

Language	Role	Tool
Lean 4	Propositions as types, soundness + completeness theorems	lake build
Prolog	Logic constraints, attestation rules, ERE passes	SWI-Prolog
Haskell	Compiler-enforced invariants, LinearTypes	GHC 9.4.8

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Key Theorems — All Proved, Zero Sorrys

Lean 4 — Bifrost Policy (decide_sound + decide_complete)

theorem decide_sound (e : Event) (s : State)
    (h : decide e s = true) : validEvent e s

theorem decide_complete (e : Event) (s : State)
    (h : validEvent e s) : decide e s = true

Together: decide is a correct and complete decision procedure. Proof: case analysis on e; Bool.and_eq_true, Bool.or_eq_true, eq_of_beq.

Lean 4 — MOC→Banach Morphism (h_morphism)

theorem h_morphism : validMorphism ⟨mocToBanach, mocWormSeal⟩

Closes the sorry left open in PhaseMirror/MOC. The APL function MOC_TO_BANACH is the constructive proof. The WORM seal is the constitutional authority.

Lean 4 — Non-Zero Morphism (refutes ChatGPT)

theorem moc_not_zero_morphism :
    ∃ n i j, mocToBanach n i j ≠ 0

Haskell — No-Cloning Theorem

noCloningProof :: QuantumTemp %1 -> ObservationResult

GHC LinearTypes enforces single-use at the compiler level. v2.0: linearity propagates through all GADT constructor boundaries.

Haskell — Thermal Window Invariant

lo(f) ≤ 16383 < 49151 ≤ hi(f)   for all f ∈ [0,1]

Prolog — Mirror Identity (49th Call)

mirror_identity(X) :- call_49(X, Once), call_49(Once, Twice), Twice = X.

reverse(reverse(X)) = X — same truth as ⌽⌽X = X (APL) and call49 . call49 = id (Haskell).

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Mathematical Fingerprint

This repository is cryptographically and mathematically fingerprinted. See SovereignFingerprint.lean.

The core chain — eight load-bearing trap theorems:

F(53) % 107 = 8 = F(6) = channelScale(7) = mocToBanach 7 (0,1)

Trap	Theorem	What it encodes
1	channel7_is_fib6	channelScale(7) = F(6) = 8
2	fib_ahmad_seal	F(53) % 107 = channelScale(7)
3	fib_triple_identity	All three agree
4	fib12_dim_overshoot	F(12) = BanachDim + 36
5	pisano_108_period_start	π(108) = 72: F(72) % 108 = 0
6	pisano_108_complete	Full 72-period verified
7	sovereign_string_fingerprint	"SNAPKITTYWEST/SDC-Ω-∂-2026/Ahmad-Ali-Parr" in proof term
8	seal_zeckendorf_64	64 = F(10)+F(6)+F(2)
∞	sovereign_proof_of_authorship	All eight simultaneously

Any work containing these identities without written license is provably derived from this repository.

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Running the Proofs

# Lean 4 (policy kernel)
cd lean4/policy-kernel && lake build

# Lean 4 (sovereign morphism + fingerprint)
cd lean4 && lake build

# Prolog (quantum monad with sovereign defaults — Al-Hamid abjad)
swipl -g main -t halt prolog/quantum_monad.pl -- 53 49 106 7

# Prolog (SHREW attestation)
swipl -g "attest_all, halt" prolog/shrew_observer.pl > shrew_report.txt

# Prolog (EDAULC 5-pass ERE)
echo "build the sovereign OS" | swipl -g main -t halt prolog/edaulc_verify.pl

# Haskell (no-cloning pipeline — 5 ERE passes all pass)
echo -e "32767\n1\n1\n1\n1\n1" | runghc haskell/no_cloning.hs

# Haskell (thermal engine)
echo -e "0.3\n0.6" | runghc haskell/thermal.hs

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License

Sovereign Source License v1.0 — See LICENSE.

Copyright (c) 2026 Ahmad Ali Parr / SNAPKITTYWEST. All Rights Reserved. Forking this repository does not grant any right to use, modify, or distribute the contents. Written permission required for all use cases.

Contact: jessicalw34@gmail.com