From 8cf61536101e6ea12ee0b8c87a220f983ea10946 Mon Sep 17 00:00:00 2001 From: mrwulf Date: Sat, 11 Jul 2026 12:26:04 +0200 Subject: [PATCH] S2 Fable-5 re-audit: close the kbelow/RFC-fidelity gap (kbelow_pow2) Adversarial statement-level re-verification of everything S2 shipped, against paper SS5.3 and the deployed Python verifier: Path recursion, Root_left/Root_right fold shapes (none exactly where the deployed code rejects), incl_complete as Theorem 1 verbatim (getD default unreachable under m < |D|), MTH([]) = H(epsilon) per RFC. All faithful. One genuine gap found and closed: the kbelow lemmas bounded k but never established k is a power of two, leaving 'our split point = the RFC split point' as by-construction folklore. kbelow_pow2 (cone: propext, Quot.sound) now pins it: 2^j = k < n <= 2k = 2^(j+1) uniquely determines the RFC 9162 split. THE button green. LTL untouched. Co-Authored-By: Claude Fable 5 --- verification/Proofs/AxiomCheck.lean | 1 + verification/Proofs/Basic.lean | 14 ++++++++++++++ verification/Proofs/Basic.olean | Bin 471896 -> 483680 bytes verification/Proofs/Completeness.olean | Bin 443272 -> 443272 bytes verification/check.sh | 1 + 5 files changed, 16 insertions(+) diff --git a/verification/Proofs/AxiomCheck.lean b/verification/Proofs/AxiomCheck.lean index 8c0d204..3e0cd9f 100644 --- a/verification/Proofs/AxiomCheck.lean +++ b/verification/Proofs/AxiomCheck.lean @@ -5,6 +5,7 @@ import Proofs.Completeness #print axioms LTLAcc.kbelow_pos #print axioms LTLAcc.kbelow_lt #print axioms LTLAcc.le_two_kbelow +#print axioms LTLAcc.kbelow_pow2 #print axioms LTLAcc.MTH #print axioms LTLAcc.Root #print axioms LTLAcc.ConsRec diff --git a/verification/Proofs/Basic.lean b/verification/Proofs/Basic.lean index 0cf4bf1..bce2c64 100644 --- a/verification/Proofs/Basic.lean +++ b/verification/Proofs/Basic.lean @@ -57,6 +57,20 @@ theorem le_two_kbelow (n : Nat) (h : 2 ≤ n) : n ≤ 2 * kbelow n := by have := ih h2 omega +/-- `kbelow` is a genuine power of two. Together with `kbelow_lt` and + `le_two_kbelow` (`2^j = k < n ≤ 2k = 2^(j+1)`) this pins `kbelow n` + as THE largest power of two strictly below `n` — the RFC 9162 split + point, uniquely determined. -/ +theorem kbelow_pow2 (n : Nat) : ∃ j, kbelow n = 2 ^ j := by + induction n using kbelow.induct with + | case1 n hle => exact ⟨0, by rw [kbelow]; simp only [if_pos hle]⟩ + | case2 n hgt ih => + obtain ⟨j, hj⟩ := ih + refine ⟨j + 1, ?_⟩ + rw [kbelow] + simp only [if_neg hgt] + rw [hj, Nat.pow_succ, Nat.mul_comm] + /-- `MTH` (paper §5.3): the RFC 9162 tree head over a leaf-data list. `MTH [] = H(ε)`, `MTH [d] = hleaf d`, and for `n ≥ 2` the split at `k = kbelow n`. -/ diff --git a/verification/Proofs/Basic.olean b/verification/Proofs/Basic.olean index 932db21fcbea16fcc1261cee49f1dfd143b77b5d..7422fe1bc139de3cbad59d2467535e75a972eb94 100644 GIT binary patch literal 483680 zcmd?Sd3?;*_dh<7MeMPsmU^KWY8e!S)nwP=wz?a2>`tbW+F_8)UuR${u^Af!J%gS<6 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zcmeBZm+oknZfId_VQOJ+VQFFA!ggT~dy;w?5PjNyeGl7BCib&uK!9cY_Wf)ZnE~nY B6}tcc delta 48 zcmeBZm+oknZfId_VQOJ+VQFFA!ggWL^n!zIY>Z#FU*E%alZo9J44AiX-_LfD834MD B5%mB7 diff --git a/verification/check.sh b/verification/check.sh index 637b463..452c047 100755 --- a/verification/check.sh +++ b/verification/check.sh @@ -26,6 +26,7 @@ declare -A CONES=( [LTLAcc.kbelow_pos]="propext, Quot.sound" [LTLAcc.kbelow_lt]="propext, Quot.sound" [LTLAcc.le_two_kbelow]="propext, Quot.sound" + [LTLAcc.kbelow_pow2]="propext, Quot.sound" [LTLAcc.MTH]="propext, LTLAcc.sha256, Quot.sound" [LTLAcc.Root]="propext, LTLAcc.sha256, Quot.sound" [LTLAcc.ConsRec]="propext, LTLAcc.sha256, Quot.sound"