mrwulf e270872a27 S3.5: explicit collision extractor — Theorem 2 made non-vacuous, vacuous forms removed ... The S3 Socratic re-audit found incl_sound was kernel-perfect but VACUOUS: its '... ∨ HasCollision' disjunct (∃ x y, x≠y ∧ sha256 x = sha256 y) is provable by pigeonhole ALONE (sha256: infinite List UInt8 → finite 32-byte Hash), so the theorem said nothing about forgeries. Even a data-carrying {p // IsCollision p} disjunct fails (Classical.choice inhabits it). The only faithful rendering of the paper's 'explicit algorithm 𝓔' is a NAMED FUNCTION whose correctness is a claim about ITS OUTPUT. - extractIncl (m D d P): total function that walks the honest tree and returns the concrete colliding preimage pair at the first divergence (a node preimage pair, or the leaf preimage pair at the bottom). - extractIncl_correct: d ≠ D[m] ∧ accepting-receipt → IsCollision (extractIncl …).1 (extractIncl …).2. A statement ABOUT the fixed function's output; pigeonhole cannot discharge it. ADVERSARIAL CHECK (probe, since removed): proved ¬ IsCollision (extractIncl 0 [[7]] [7] []) — i.e. on a NON-forgery input the output is provably NOT a collision, so the conclusion is genuinely false for some inputs ⇒ non-vacuous, choice-proof. - Removed the vacuous theorems entirely (incl_sound, root_binding, hnode/hleaf_inj_or_collision, HasCollision def) so no hollow statement survives in a corpus destined for the log. Kept the real building blocks (hnode_preimage_inj [propext]; eq_dropLast helper moved to Completeness; Binding.lean deleted). extractIncl_correct cone [propext, Classical.choice, LTLAcc.sha256, Quot.sound]. THE button green (14 certs). Fable statement-audit passed. LTL untouched (12 leaves, bcd15f9d). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>		2026-07-11 15:31:21 +02:00
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gen/LTLAcc	S3/L4-L5: root binding (Lemma 2, Path instance) + Theorem 2, constructive	2026-07-11 13:21:17 +02:00
Proofs	S3.5: explicit collision extractor — Theorem 2 made non-vacuous, vacuous forms removed	2026-07-11 15:31:21 +02:00
check.sh	S3.5: explicit collision extractor — Theorem 2 made non-vacuous, vacuous forms removed	2026-07-11 15:31:21 +02:00
lean-guard	L1+L2: hashing shapes, domain separation, MTH/Root/ConsRec with termination	2026-07-10 23:58:00 +02:00