mrwulf be232507cc S4: descent extractor extractMTH (Theorem 3 step 3 + F2 restoration), non-vacuous ... The 'descend' step of the paper's Theorem 3, built extractor-first per the S3.5 lesson (never a bare '∨ collision'): - extractMTH (D D'): total function that, given two equal-length leaf lists sharing a Merkle root, walks the common-shape tree to the first divergence and returns the concrete colliding preimage pair (a node pair, or a leaf pair at the bottom). - extractMTH_correct: |D|=|D'| ∧ D≠D' ∧ MTH D = MTH D' → IsCollision (extractMTH D D'). Proven by functional induction on extractMTH; composite case uses MTH_split + append_inj (fixed-width Hash) to split node preimages or exhibit the node collision. - extractMTH_nonvacuous: equal lists → output NOT a collision (pinned), so the conclusion is false for some inputs ⇒ choice-proof. This also RESTORES, in explicit non-vacuous form, the receipt-uniqueness content of Lemma 2 deleted in the S3.5 cleanup (re-audit F2): the honest Merkle fold is injective up to a collision. 18 certs green. Fable statement-audit passed (matches paper Thm 3 step 3 verbatim). LTL untouched (12 leaves, bcd15f9d). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>		2026-07-11 16:46:58 +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	S4: descent extractor extractMTH (Theorem 3 step 3 + F2 restoration), non-vacuous	2026-07-11 16:46:58 +02:00
check.sh	S4: descent extractor extractMTH (Theorem 3 step 3 + F2 restoration), non-vacuous	2026-07-11 16:46:58 +02:00
lean-guard	L1+L2: hashing shapes, domain separation, MTH/Root/ConsRec with termination	2026-07-10 23:58:00 +02:00