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mrwulf
eb3df7503f
The crux layer — the statement whose HAND proof once carried the frontier
coverage bug is now kernel-checked.
- gen: hash outputs refactored to Hash = {l : List UInt8 // l.length = 32}.
MECHANIZATION FINDING: the paper's pair-coincidence step ('equal hnode
values of distinct argument pairs are a collision') is load-bearing on
FIXED-WIDTH outputs — with unconstrained byte strings x++s = X++Y does
not split. hnode_preimage_inj (cone: propext) makes this explicit via
List.append_inj on equal-length components. Queued as a half-sentence
for the paper's next cycle.
- HasCollision := ∃ x y, x ≠ y ∧ sha256 x = sha256 y — appears ONLY as a
conclusion, never a hypothesis (no collision-resistance assumed).
- hnode_inj_or_collision / hleaf_inj_or_collision: the per-node dichotomy.
- root_binding: any accepting reconstruction from (v,P) to the honest root
either IS the honest receipt (leaf hash AND full path P = Path m D — case
(ii) pinning every consumed sibling) or exhibits a collision. Motive
quantifies (v,P); induction on Path; k-fold discipline.
- incl_sound (Theorem 2, position binding): accepting a wrong leaf at m
yields a collision. Cone [propext, Classical.choice, LTLAcc.sha256,
Quot.sound] — the single hash axiom, pinned in check.sh. ALL GREEN.
Also: Root n=1 branch changed from list-match to decidable 'if P = []'
(well-founded unfolding generated a spurious exhaustiveness obligation);
Root_one_cons added. Fable-5 statement-audit passed. LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
22 lines
914 B
Text
22 lines
914 B
Text
/- The single sanctioned axiom site of this corpus (mirrors the role of
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gen/ in the *-ed25519-verified repos): SHA-256 as an opaque function
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into 32-byte outputs. No properties are assumed of it — in particular
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NOT collision resistance; the soundness theorems downstream are
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constructive, they EXHIBIT two distinct preimages with equal image.
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The fixed output WIDTH is part of the function's type, not an
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assumption about its behavior: it is what makes hnode argument pairs
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recoverable from preimages (the paper's "65-byte preimages"
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parenthetical, made explicit). -/
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namespace LTLAcc
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/-- A 32-byte hash value. -/
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def Hash : Type := { l : List UInt8 // l.length = 32 }
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instance : Inhabited Hash := ⟨⟨List.replicate 32 0, by simp⟩⟩
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instance : DecidableEq Hash := fun a b =>
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decidable_of_iff (a.val = b.val) Subtype.ext_iff.symm
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axiom sha256 : List UInt8 → Hash
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end LTLAcc
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