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mrwulf
02a45eae36
The paper's hardest theorem is fully kernel-checked. extractCons joins the two proven halves: extractConsNode's collision (via consRecBinding, steps 1-2) or the descent extractMTH D₀ (D₁.take n₀) (step 3, S4). - extractCons_correct: acceptance ConsRec n₀ |D₁| C ⊤ (MTH D₀) = some (MTH D₀, MTH D₁) with D₀ ≠ D₁.take n₀ (and |D₀| = n₀ ≤ |D₁|, 0 < n₀) ⇒ IsCollision of THIS function's output. Statement matches paper Thm 3 verbatim (the n₀ = 0 escape is vacuous there: [] is always the real prefix). Compiled on first attempt — the pre-verified skeleton held exactly. - extractCons_nonvacuous (queued requirement honored): on a non-rewrite input the output is provably NOT a collision — choice-proof. Cones: extractCons_correct [propext, Classical.choice, LTLAcc.sha256, Quot.sound] — single hash axiom, no collision-resistance assumed anywhere. 29 certs green. Fable statement-audit passed. LTL untouched (12 leaves, bcd15f9d). Corpus now holds kernel-checked: Lemma 1, Theorem 1, Theorem 2, Theorem 3 (+ whole-tree Lemma 2). Remaining: Prop 1 (S6), fidelity harness (S7), freeze (S8). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
67 lines
3.1 KiB
Text
67 lines
3.1 KiB
Text
/- S5.4 — **Theorem 3 (Consistency soundness)**, assembled: the explicit
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extractor 𝓔′ for history rewrites. Joins consRecBinding (steps 1-2,
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S5.3) to extractMTH (step 3, S4).
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Statement design per the corpus discipline: a NAMED function whose
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correctness is about ITS OUTPUT (pigeonhole/choice cannot discharge
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it), guarded by a permanent non-vacuity witness. -/
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import Proofs.Binding3
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namespace LTLAcc
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/-- The consistency extractor 𝓔′ (paper Theorem 3). On a claimed rewrite
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— an accepted consistency proof `C` between the pinned root of `D₀`
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and the head of `D₁`, where `D₀` is NOT the real prefix — return the
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node collision found while walking the fold, or descend into the two
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same-root prefix trees. -/
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noncomputable def extractCons (n₀ : Nat) (C : List Hash)
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(D₀ D₁ : List Bytes) : List UInt8 × List UInt8 :=
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match extractConsNode n₀ D₁.length C true (MTH D₀) D₁ with
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| some c => c
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| none => extractMTH D₀ (D₁.take n₀)
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/-- **Theorem 3 (Consistency soundness), explicit form**: if the
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consumer's verifier accepts `C` between the pinned head `MTH D₀`
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(size `n₀`) and the offered head `MTH D₁`, but `D₀` is not the real
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prefix of `D₁`, then `extractCons` outputs a genuine SHA-256
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collision. -/
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theorem extractCons_correct (n₀ : Nat) (C : List Hash) (D₀ D₁ : List Bytes)
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(hlen0 : D₀.length = n₀) (hn0 : 0 < n₀) (hle : n₀ ≤ D₁.length)
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(hne : D₀ ≠ D₁.take n₀)
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(hacc : ConsRec n₀ D₁.length C true (MTH D₀) = some (MTH D₀, MTH D₁)) :
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IsCollision (extractCons n₀ C D₀ D₁).1 (extractCons n₀ C D₀ D₁).2 := by
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have hbind := consRecBinding (MTH D₀) n₀ D₁.length C true D₁
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(MTH D₀) (MTH D₁) rfl hn0 hle hacc rfl
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rw [extractCons]
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cases hrec : extractConsNode n₀ D₁.length C true (MTH D₀) D₁ with
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| some c =>
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rw [hrec] at hbind
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exact hbind
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| none =>
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rw [hrec] at hbind
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-- hbind : MTH D₀ = MTH (D₁.take n₀); descend
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have htklen : (D₁.take n₀).length = n₀ := by
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rw [List.length_take]; omega
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exact extractMTH_correct D₀ (D₁.take n₀) (by omega) hne hbind
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/-- Permanent non-vacuity witness: on a NON-rewrite input (the pinned
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list IS the real prefix), the extractor's output is provably NOT a
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collision — so the correctness conclusion is false for some inputs
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and cannot be discharged by pigeonhole or choice. Uses the honest
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n₀ = n base: D₀ = D₁ = [[7]], C = [], where ConsRec accepts and
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extractConsNode returns none, so extractCons = extractMTH D₀ D₀ =
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the equal leaf pair. -/
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theorem extractCons_nonvacuous :
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¬ IsCollision (extractCons 1 [] [([7] : List UInt8)] [([7] : List UInt8)]).1
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(extractCons 1 [] [([7] : List UInt8)] [([7] : List UInt8)]).2 := by
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rw [extractCons]
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have hrec : extractConsNode 1 ([([7] : List UInt8)]).length [] true
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(MTH [([7] : List UInt8)]) [([7] : List UInt8)] = none := by
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rw [extractConsNode]; simp
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rw [hrec]
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rw [extractMTH]
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simp only [List.length_singleton, if_pos (by omega : (1:Nat) ≤ 1)]
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intro hcol
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exact hcol.1 rfl
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end LTLAcc
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