From cfde9b2cd79bdd8e5bbafa0ad98d6494a4eca046 Mon Sep 17 00:00:00 2001 From: mrwulf Date: Sat, 11 Jul 2026 17:55:51 +0200 Subject: [PATCH] S5 stage 2: extractConsNode extractor defined (consistency, Theorem 3 steps 1-2) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The consistency collision extractor: walks the ConsRec new-root fold in parallel with the honest size-n tree of D₁ and returns the concrete colliding node preimage pair at the first level where the fold's hnode argument pair diverges from the honest node — or none if the fold is genuine all the way down (binding holds). Both branches verified faithful to ConsRec's hnode argument order (n₀≤k: y' left / s right; n₀>k: s left / y' right). Termination via kbelow bounds. Deliberate honest checkpoint: the DEFINITION compiles and is cone-audited [propext, LTLAcc.sha256, Quot.sound]; the binding CORRECTNESS proof — the single hardest object in the corpus — is stage 3, kept for a fresh session rather than a rushed long turn. 22 certs green. LTL untouched. Co-Authored-By: Claude Fable 5 --- README.md | 2 +- verification/Proofs/AxiomCheck.lean | 1 + verification/Proofs/Consistency.lean | 39 ++++++++++++++++++++++++++ verification/Proofs/Consistency.olean | Bin 148488 -> 348920 bytes verification/check.sh | 1 + 5 files changed, 42 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index f808711..7c9a182 100644 --- a/README.md +++ b/README.md @@ -16,7 +16,7 @@ the same discipline as the four `*-ed25519-verified` subject corpora. | L5 | inclusion soundness = EXPLICIT extractor `extractIncl` (Theorem 2) **done, non-vacuous** | | L6a | descent extractor `extractMTH` (Theorem 3 step 3 = Lemma 2, WHOLE-TREE instance) **done, non-vacuous** | | — | Lemma 2, PATH instance (receipt-uniqueness of `Root`): deleted with the vacuous `root_binding` in S3.5 and **not yet restored**; optional, not needed for Theorem 3 | -| L6b | ConsRec binding + Theorem 3 assembly (extractCons) | in progress (S5): stage-1 arithmetic/list infrastructure done (kbelow_prefix_eq, take surgery); binding + assembly next | +| L6b | ConsRec binding + Theorem 3 assembly (extractCons) | in progress (S5): stage-1 arithmetic/list infrastructure done (kbelow_prefix_eq, take surgery); stage-1 infra + extractConsNode extractor DEFINED; binding proof (steps 1-2) + extractCons assembly = stage 3 | | L6 | pin-store state machine safety (Proposition 1) | pending | ## Discipline (identical to the subject corpora) diff --git a/verification/Proofs/AxiomCheck.lean b/verification/Proofs/AxiomCheck.lean index 202c3fa..6fd10d5 100644 --- a/verification/Proofs/AxiomCheck.lean +++ b/verification/Proofs/AxiomCheck.lean @@ -25,3 +25,4 @@ import Proofs.Consistency #print axioms LTLAcc.kbelow_prefix_eq #print axioms LTLAcc.take_take_le #print axioms LTLAcc.take_drop_prefix +#print axioms LTLAcc.extractConsNode diff --git a/verification/Proofs/Consistency.lean b/verification/Proofs/Consistency.lean index c91af52..43c3026 100644 --- a/verification/Proofs/Consistency.lean +++ b/verification/Proofs/Consistency.lean @@ -64,4 +64,43 @@ theorem take_drop_prefix (l : List Bytes) (k n₀ : Nat) : (l.take n₀).drop k = (l.drop k).take (n₀ - k) := by rw [List.drop_take] +/-! ### the consistency collision extractor (paper Theorem 3, steps 1-2) -/ + +/-- Walk the `ConsRec` fold in parallel with the honest size-`n` tree of + `D₁`. At each level the new-root component builds `hnode` of a left and + a right value; compare that argument pair against the honest node + `hnode (MTH (D₁.take k)) (MTH (D₁.drop k))`. Return `some` concrete + colliding preimage pair at the first mismatch (steps 1-2 of Theorem 3), + or `none` if the fold is genuine all the way down — in which case the + binding `x = MTH (D₁.take n₀)` holds (proven in stage 3). -/ +noncomputable def extractConsNode (n₀ n : Nat) (C : List Hash) (b : Bool) + (r : Hash) (D₁ : List Bytes) : Option (List UInt8 × List UInt8) := + if n₀ = n then none + else if n₀ > n ∨ n₀ = 0 ∨ n ≤ 1 then none + else + match C.getLast? with + | none => none + | some s => + let k := kbelow n + if n₀ ≤ k then + let y' := ((ConsRec n₀ k C.dropLast b r).map Prod.snd).getD default + if y' = MTH (D₁.take k) ∧ s = MTH (D₁.drop k) then + extractConsNode n₀ k C.dropLast b r (D₁.take k) + else + some (0x01 :: (y'.val ++ s.val), + 0x01 :: ((MTH (D₁.take k)).val ++ (MTH (D₁.drop k)).val)) + else + let y' := ((ConsRec (n₀ - k) (n - k) C.dropLast false r).map Prod.snd).getD default + if s = MTH (D₁.take k) ∧ y' = MTH (D₁.drop k) then + extractConsNode (n₀ - k) (n - k) C.dropLast false r (D₁.drop k) + else + some (0x01 :: (s.val ++ y'.val), + 0x01 :: ((MTH (D₁.take k)).val ++ (MTH (D₁.drop k)).val)) +termination_by n +decreasing_by + · have h2 : 2 ≤ n := by omega + exact kbelow_lt n h2 + · have := kbelow_pos n + omega + end LTLAcc diff --git a/verification/Proofs/Consistency.olean b/verification/Proofs/Consistency.olean index 50cc8997599a384dba8b88891eeed433de96c7eb..c8ff9c7f8deab7168204da1f5fcee53c1e0be747 100644 GIT binary patch literal 348920 zcmbS!d3?;*_x>P>v5!598dQyLdEqG`;w#)xTej@Sxz}zIFT8>>nHvJ|LoIo$z}7`qzu-SFdlK;QsY$)#%&5 zUcY`O)4ZeATboSD9Ts}1l9t0{dg2eUq<;9jWz?Wi_^-)o%9+Ec>v?PWkF+Zh{0#$&1#B=O~~>N7fO(D2a_o>Hk_JmjtHK4;3pCKuXL9`z#qhkjxp zD0!)nlL=aW!|0diwEyt&|17T-6gG&IXV0bWUUlKeB0pX~y@>K?Cn@cXh#oZ}yx*v% z!=gsE9oGM!_Qpcq#w{C*pMAAhS;}LakTPBjzlDz&r*%_$C4)a5blbt+J3db>@+;-! z(N#^P91rMM;Wcfi*-zVN18s7)_xLVxfhQ=>Gq8<6NJ~LJ;xA%&A0t{ko!mEK)YyoK zDBz07evXFxU4?f~PAIWjE9u*r#f`d$Wakd{m>ak z9VIUW@|>U_zfw6oxkNw@CBwjT#-ZGh?Rj2%cp14r@&~8%N 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