mrwulf 02a45eae36 S5.4: THEOREM 3 COMPLETE — extractCons assembly + non-vacuity witness ...

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>

2026-07-11 20:07:20 +02:00

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