Re-derived S5.3 (all done under an Opus switch) from zero. consRecBinding
STATEMENT re-confirmed faithful to paper Thm 3 steps 1-2 (y=MTH D₁ = the
hash-fold condition; some=>collision / none=>x=MTH(D₁.take n₀) = the two
Lemma-2 outcomes); non-vacuous (some-branch is a SPECIFIC-pair IsCollision,
not pigeonhole-provable; none-branch a real equality needing hcons).
FINDING + FIX: Opus changed ConsRec's base definition (list-match →
decidable if) with only 'recompiled clean' as evidence — a definition
that mirrors the deployed verifier. Now machine-checked: consRec_base_
false_eq / consRec_base_true_eq prove the decidable-if base EQUALS the
exact list-match forms it replaced. Kept as PERMANENT cone-audited
theorems (F1 discipline: keep the evidence), not a throwaway probe.
QUEUED for S5.4: extractCons_correct (Theorem 3 endpoint) MUST carry a
permanent non-vacuity witness like extractIncl_nonvacuous/extractMTH_
nonvacuous. S7 must re-confirm the NEW ConsRec base vs Python.
26 certs green. LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
