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mrwulf
43f2c40cac
The consumer pin store (§5.4) as a transition predicate; the paper's Prop 1(1) fully mechanized: - pinAccept: same-size ⇒ root match; smaller ⇒ reject (rollback); larger ⇒ consistency proof verifies. Mirrors sthstore.py. - pinAccept_monotone: an accepted step never shrinks the pin (definitional). - pin_prefix_correct: an honest advance where D is NOT the prefix of D' makes pinExtract output a genuine collision — same-size routes to extractMTH (whole-tree Lemma 2), grow routes to extractCons (Theorem 3). Explicit named-extractor form ⇒ non-vacuous (pin_prefix_nonvacuous pinned). - fork_distinct: the Merkle share of Prop 1(2) — different roots at equal size commit to different content. EUF-CMA transferable-evidence is signature-layer, OUT OF SCOPE and documented in the file header (not smuggled). Cones: single hash axiom (pin_prefix_correct adds Classical.choice via functional induction downstream). 33 certs green. Fable statement-audit: matches paper Prop 1(1); Prop 1(2) scope-bounded honestly. LTL untouched. Every §6 statement is now kernel-checked: Lemma 1, Theorems 1-3, whole-tree Lemma 2, Proposition 1. Remaining: S7 fidelity, S8 freeze. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
93 lines
4.4 KiB
Text
93 lines
4.4 KiB
Text
/- S6 — **Proposition 1 (Pin-store safety)**, the Merkle-layer contribution.
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The consumer pin store (§5.4) as a transition predicate; monotonicity is
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definitional, and prefix-ordering — the substantive part — reduces to
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Theorem 3 (grow) and the whole-tree Lemma 2 (same-size), stated as an
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explicit named-extractor collision (non-vacuous), never a bare ∃.
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SCOPE: Ed25519 EUF-CMA is NOT in this corpus (signatures are abstract).
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Part (2) of the paper's Prop 1 — that two conflicting signed heads are
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*transferable* evidence — is a signature-layer fact; the Merkle layer
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contributes only that different roots at equal size commit to different
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content (fork_distinct). This boundary is documented, not smuggled. -/
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import Proofs.Theorem3
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namespace LTLAcc
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/-- The pin-store accept predicate (§5.4): same size ⇒ root must match;
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smaller ⇒ reject (rollback); larger ⇒ a consistency proof from the
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pinned head must verify. Mirrors sthstore.py. -/
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def pinAccept (n : Nat) (r : Hash) (n' : Nat) (r' : Hash) (C : List Hash) : Prop :=
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if n' = n then r' = r
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else if n' < n then False
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else ConsRec n n' C true r = some (r, r')
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/-- **Monotonicity (size)**: an accepted step never shrinks the pin. -/
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theorem pinAccept_monotone (n : Nat) (r : Hash) (n' : Nat) (r' : Hash)
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(C : List Hash) (h : pinAccept n r n' r' C) : n ≤ n' := by
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unfold pinAccept at h
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by_cases he : n' = n
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· omega
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· by_cases hl : n' < n
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· simp [he, hl] at h
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· omega
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/-- The pin-store collision extractor: whole-tree descent at equal size,
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else the consistency extractor. -/
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noncomputable def pinExtract (n n' : Nat) (C : List Hash)
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(D D' : List Bytes) : List UInt8 × List UInt8 :=
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if n' = n then extractMTH D D' else extractCons n C D D'
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/-- **Prefix-ordering (monotonicity, content)**: if the pin advances from an
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honest head of `D` to an honest head of `D'` but `D` is NOT the prefix
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of `D'` of its length, then `pinExtract` outputs a genuine collision.
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(Explicit form ⇒ non-vacuous; this is the paper's Prop 1(1).) -/
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theorem pin_prefix_correct (n n' : Nat) (r r' : Hash) (C : List Hash)
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(D D' : List Bytes)
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(hstep : pinAccept n r n' r' C)
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(hDlen : D.length = n) (hDr : MTH D = r)
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(hD'len : D'.length = n') (hD'r : MTH D' = r')
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(hn0 : 0 < n) (hne : D ≠ D'.take n) :
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IsCollision (pinExtract n n' C D D').1 (pinExtract n n' C D D').2 := by
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unfold pinAccept at hstep
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by_cases he : n' = n
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· -- same size: r' = r ⇒ MTH D' = MTH D; D ≠ D'.take n = D' (len n)
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simp only [if_pos he] at hstep
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rw [pinExtract]; simp only [if_pos he]
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have hlen : D.length = D'.length := by rw [hDlen, hD'len, he]
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have hroot : MTH D = MTH D' := by rw [hDr, hD'r, hstep]
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have hne' : D ≠ D' := by
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intro h; apply hne; rw [h]
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have hta : D'.take n = D' := by apply take_all; rw [hD'len]; exact he
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rw [hta]
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exact extractMTH_correct D D' hlen hne' hroot
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· by_cases hl : n' < n
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· simp [he, hl] at hstep
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· -- grow: ConsRec n n' C true r = some (r, r')
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have hgrow : ConsRec n n' C true r = some (r, r') := by
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simp only [he, hl, if_false] at hstep; exact hstep
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rw [pinExtract]; simp only [if_neg he]
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have hle : n ≤ D'.length := by omega
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have hacc : ConsRec n D'.length C true (MTH D) = some (MTH D, MTH D') := by
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rw [hDr, hD'r, hD'len]; exact hgrow
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exact extractCons_correct n C D D' hDlen hn0 hle hne hacc
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/-- **Fork observation (Merkle-layer share of Prop 1(2))**: two honest
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heads of equal size with different roots commit to different content.
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(Transferable-evidence via EUF-CMA is signature-layer, out of scope.) -/
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theorem fork_distinct (n : Nat) (r r' : Hash) (D D' : List Bytes)
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(hDlen : D.length = n) (hD'len : D'.length = n)
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(hDr : MTH D = r) (hD'r : MTH D' = r') (hrne : r ≠ r') : D ≠ D' := by
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intro h; apply hrne; rw [← hDr, ← hD'r, h]
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/-- Permanent non-vacuity witness for pin_prefix_correct: on an honest
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non-fork step (D IS the prefix), the extractor output is not a
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collision. Uses the same-size identity D = D' = [[7]]. -/
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theorem pin_prefix_nonvacuous :
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¬ IsCollision (pinExtract 1 1 [] [([7] : List UInt8)] [([7] : List UInt8)]).1
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(pinExtract 1 1 [] [([7] : List UInt8)] [([7] : List UInt8)]).2 := by
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rw [pinExtract]; simp only [if_pos rfl]
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rw [extractMTH]; simp only [List.length_singleton, if_pos (by omega : (1:Nat) ≤ 1)]
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intro hcol; exact hcol.1 rfl
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end LTLAcc
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