THE DEFECT, demonstrated by a reviewer with a working payload. The driver
surface is reported by an `#eval` inside Proofs/Inventory.lean. Anything
declared AFTER that command is in the compiled object file but does not exist
in the environment while the command runs, so the walk cannot see it. The
reviewer appended
def bait : Nat := 0
theorem bait.smuggled : forall n : Nat, n + 0 = n := ...
re-pinned, and ran the button. It printed "no axiom, no claim", the statement
digest was BYTE-IDENTICAL to the clean tree, and the run went green — while a
theorem with a real axiom cone sat in the environment. In neither walk: not
corpus, because an instrument is not corpus; not driver surface, because it
post-dates the emitter. In no allowlist. Pinned by nothing.
This repository also had no kernel-side scan at all. Its axiom gate was a
source-text grep, evadable by a leading space — which its own selftest case 12
already exploited.
THE FIX, ported from the ed25519 forks:
· a kernel-side axiom-declaration gate that reads every compiled .olean via
readModuleData. It sees what was actually stored, regardless of
indentation, attributes, privacy, or where a declaration sits relative to
any #eval. Membership self-derives from the manifest and the module count
must match, so a deleted artifact cannot make the scan vacuous.
· the ACCOUNTING IDENTITY, as set containment:
every constant the kernel sees in corpus inventory union instrument surface
The two walks read ENVIRONMENTS; the gate reads OBJECT FILES. What a walk
cannot see because of where it sits in a file, the object file still holds.
That asymmetry is the entire content of this fix.
Compared as SETS deliberately. Counts cannot express the relation — an
object file may hold two physical copies of one lazily-materialised
equation lemma while an environment holds one constant per name — and
arithmetic between those views misled the ed25519 version twice before it
was stated as containment.
PLACEMENT differs from the forks, for a reason worth recording: there the
audit drivers are members of the compile manifest, so a gate beside the
compile phase finds them. Here AxiomCheck is compiled by Phase 3 and Inventory
by Phase 3b, so an earlier gate fails on a missing artifact — which it did,
correctly, on the first port. It runs inside Phase 3b, because the instruments
are exactly what it must see.
VERIFIED with the reviewer's own payload, which previously went green:
ACCOUNTING FAILED: the kernel holds constants that neither walk accounts for:
bait
bait.smuggled
selftest_audit.sh: 14 attack cases -> 15. Note in the new case, because it
cost two iterations: `theorem bait.smuggled : True := trivial` does NOT
exercise this gate — Phase 1's stub audit greps for `: True :=` and catches it
first. Real defence in depth, but the naive payload never reaches the gate
under test, so the case uses the reviewer's original.
Two residues fixed while adding it, both the same shape: a case that was last
when written, leaving state the next case inherits. Case 13 restored
AxiomCheck.lean but not its pin; case 9 left its rogue gen file. Fixed at the
point of use so each case keeps testing what it tested before.
Button green (234 declarations across 11 modules, all accounted for),
15/15 self-test green, ATTESTATION GREEN with fidelity.
P0-a was applied to the four ed25519 repositories on 2026-07-30 and never
here. Found by the control repo's capability matrix, which asks the property
rather than looking for a phase by name.
The finding that made it matter there applies verbatim: a verification that
never cleans up cannot distinguish "these proofs check" from "these proofs
check GIVEN WHATEVER IS LYING AROUND". Compiled artifacts are gitignored, so
no `git status` can show a reader that a verdict rested on an object from an
earlier run of a different script.
This repository has no --audit-only mode, so the purge is unconditional.
Button green (80s) and the 14-case self-test green after the change.
CLASS 15 — a Lean file where no phase was looking. The dead-file scan read
Proofs/*.lean and gen/LTLAcc/*.lean and nothing else. A module at the
verification root, or under any other gen/ subdirectory, was neither
compiled nor rejected — while remaining importable by name, since LEAN_PATH
contains both roots. That is a source of the corpus that no phase reads and
no pin covers, which is exactly what the dead-file gate exists to forbid; it
was simply looking in two places instead of everywhere. Now nothing may live
in either root but the two enumerated sets.
CLASS 9 — the instruments' own declaration surface. AxiomCheck.lean and
Inventory.lean perform the audit and are therefore not corpus, so nothing
inventoried what THEY declare. Inventory.lean now walks both: AxiomCheck by
module index, and itself as the module still being elaborated, whose
declarations are the ones the environment reports with no originating
module. That is what makes the inventory cover the instrument that produces
it rather than exempting itself.
The policy is not "declare nothing" — this file legitimately declares its
machinery. It is that an instrument may declare only inert definitions. An
axiom here would widen the trusted base without appearing in any
certificate's cone; a theorem here would be a claim no certificate covers
and no allowlist pins. A flat ban on theorems was WRONG and was measured to
be wrong: defining a function by well-founded recursion makes the elaborator
emit its own obligations, and axiomCone._proof_1 rejected this very file.
The distinction that holds is whether a theorem is a claim someone wrote or
an artefact of a definition declared alongside it — an artefact's name
extends the name of a constant declared with it.
Observed surface: 18 declarations, 16 def and 2 generated obligations, no
axiom, no standalone claim.
The drivers are byte-pinned already, so this does not pin WHICH definitions
they contain — that would add a thing to maintain without adding a thing to
catch. It adds the property byte-pinning cannot give: that no instrument
declares an axiom or a claim, whatever its bytes are.
selftest_audit.sh: 10 cases -> 14. Case 12 uses an INDENTED axiom, because
Phase 1's source grep catches an unindented one and the point is to reach
the kernel-side walk standing behind it.
TWO DEFECTS IN THE TEST HARNESS, found while adding the cases.
· The scratch tree copied verification/ only, but the button also reads
README.md and STATEMENT-MAP.md from the repository root. check.sh
therefore ALWAYS died in Phase 3c in the scratch tree, which made every
`if check.sh; then <attack not caught>` guard unfirable — check.sh could
not pass in there even with no attack at all. Only the diagnostic greps
were doing any work. The documents are now copied, and the negative test
below proves the guard is live: with the driver-surface check disabled,
check.sh PASSES a tree whose inventory driver declares
`axiom driver_cheat : False`.
· Case 9 was the last case when it was written and left its rogue gen file
in place. Harmless then; the new cases inherited it. Cleaned up between
the blocks rather than inside case 9, so that case still tests what it did.
Also fixed while here: Phase 3b compared the compile manifest against
Inventory.lean by grepping the WHOLE FILE for a backticked module name, so
prose counted — a doc comment naming a module broke the count, and in the
other direction a doc mention of a module missing from the array would have
satisfied the presence check and hidden the omission. It now reads the
arrays.
Both new gates negative-tested by removal. Button green, self-test green.
This repository has the estate's strongest gates, which makes them the most
valuable to switch off. Until now every one of them was executed by scripts
that nothing pinned.
Phase 0c requires every harness file to match HARNESS.sha256 — 15 files:
check.sh, lean-guard, inventory_gate.sh, run_bare.sh, all three self-tests,
both audit drivers (Proofs/Inventory.lean, Proofs/AxiomCheck.lean), the policy
tables (inventory-allowlist.txt, AUDIT-MANIFEST.txt), the toolchain pin, the
fidelity harness and its Python transcription, and the extracted model.
WHICH files must be pinned is policy and lives in check.sh, never in the map
being consulted: the required set is derived from the filesystem (the
executable bit, plus gen/**.lean, plus an explicit list for the rest), so
deleting a pin entry is a set mismatch rather than a silent un-pinning.
gen/LTLAcc/HashExternal.lean was previously bound by nothing at all — it was
compiled and trusted. It is now pinned, and the derivation is by set, so a new
model file fails closed.
selftest_audit.sh case 9 is split rather than relabelled. Phase 0c now catches
an unpinned rogue gen module BEFORE the dead-file gate runs, so asserting only
the new diagnostic would have quietly retired the dead-file gate from the test
suite. 9a asserts the harness-set mismatch on the unpinned file; 9b pins it —
an author who added it deliberately — and asserts Phase 2 still dies with DEAD
FILE (gen). Ten cases now, all defeated.
KNOWN-GAPS and the trusted base record the circularity plainly: an author who
edits a script and refreshes its pin in one commit passes every phase. The pin
removes the silent path, not the possibility. Review at the pinned commit
remains the consumer's protection.
Verified green after the fix: button (75s), harness self-test, binding
self-test, and the ten-case audit self-test. ATTESTATION GREEN (Lean +
fidelity), all fidelity case counts identical to the pre-change run.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
STATEMENT BINDING (Phase 3d). The coverage gate pins every constant's name,
kind and axiom cone, both directions, and none of selftest_audit.sh's nine
attacks defeat it. It is nevertheless blind to what a declaration SAYS — and
that is demonstrated here rather than argued:
Wrapping one branch of `LTLAcc.pinAccept`'s body in `id (…)` is
definitionally equal. Every downstream proof still compiles. The name, the
kind, the type and the axiom cone are unchanged. The inventory gate reports
"222 constants, environment == allowlist" — GREEN.
That edit is harmless by construction; the point is that nothing stood between
it and a genuinely vacuous redefinition of a specification. Proofs/Inventory.lean
now also emits, for every inventoried constant, its fully-elaborated TYPE, and
for every definition its fully-elaborated BODY — 266 lines over 222 constants.
Proof terms are deliberately absent: by proof irrelevance a theorem's content
is its statement. check.sh Phase 3d binds the SHA-256 and the block is
committed as AUDIT-MANIFEST.txt so a mismatch is DIFFED, not merely reported.
The existing gate is untouched, per the standing rule that the port flows FROM
this repo, not to it: INV lines are byte-identical, inventory_gate.sh is
unchanged, and all nine of its attacks still fail as before.
selftest_statements.sh replays the defeq edit as case 1, asserting BOTH that
the coverage gate passes it and that Phase 3d catches it — so if the coverage
gate ever grows to see this, the test says so instead of quietly re-labelling.
Cases 2-4 cover a hand-edited committed block, a truncated block, and a
constant inventoried without a statement.
FIDELITY PIN (unrelated, found while running the button). Phase 4 had been
failing since 2026-07-23: LIED_PIN_DIV expected 3,867 divergences between the
Lean model and the deployed consistency verifier, and observed 0. Cause is
pacta ddbb5a4, which restored the RFC 9162 2.1.4.2 Step-7 terminal `sn == 0`
condition; that one conjunct removes every divergence in the pinned
73,573-case family. KNOWN-GAPS gap 14 already recorded the closure on the day
it landed — only this constant was stale, so the button had been red for five
days with nobody running it. The pin now reads 0 with the history in a comment.
Nothing about the paper, public log entry 13, or the attested commit 172a1d0
changes; the historical divergence stays reproducible at the tagged pre-fix
commit.
KNOWN-GAPS gap 16 records what the binding does not buy: identity, not
meaning; an author who edits and re-pins in one commit is caught by review and
not by the script; and proof terms are unbound by design.
Button green end to end: ATTESTATION GREEN (Lean + fidelity).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Round-4 verdicts: Claude reviewer — nothing blocks the freeze, no
remaining findings; GPT-5.6 — approve after minor documentation fixes,
attestation scoped to the mechanized model. This round is those fixes;
no Lean surface changed.
- 218/59 → 222/61 everywhere, and STRUCTURALLY: check.sh Phase 3c
asserts the audit counts (STATEMENT-MAP + README vs allowlist/CONES)
and the four fidelity pins (STATEMENT-MAP vs run_fidelity.py
constants) on every run — stale-count drift is a red button now
(R4-1, third recurrence of the class).
- Gap 14 reworded to evidence-vs-inference (the invariant "is assumed",
not "transfers"), witnesses cited (paper §5.3/§5.4; pacta
sthstore.py/logclient.py — outside the fidelity target). New gap 15:
deployment refinement invariant unmechanized (GPT's principal
finding, split out because it carries the deployed-soundness claim).
- Runbook: A1 marked done (both approvals on SD); B2 gains the REQUIRED
scoped attestation wording (GPT §11) as a gate condition — entry 13
cannot claim "deployed verifier formally verified".
- run_bare.sh fail-closes on Lean version AND commit (rejection path
tested with a fake toolchain: FATAL, exit 1).
- Harness: "consistency baseline family" line (GPT §8); gap 14 says
"fixed offsets n−1/n+1/n+7" (R4-5).
- RESPONSE round 5, incl. refutation of GPT §7 (the target tarball
demonstrably contains MANIFEST.sha256 + TARGET-PROVENANCE.md; the
round-5 kit also ships both unpacked as a courtesy).
check.sh exit 0 ATTESTATION GREEN (Phases 0-4 incl. new 3c); selftest
exit 0, 9/9 + control. Live LTL untouched (12 leaves, bcd15f9d…).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Round-3 verdicts: GPT-5.6 conditionally approves (blockers closed, one
portability finding); the Claude reviewer's Socratic addendum produced
F1*, the strongest finding of the series — deployed verify_consistency
and mechanized ConsRec are NOT extensionally equal. Reproduced exactly
(witness verify_consistency(1,3,R2,R3,P(2→3))=True vs ConsRec reject;
3,405 divergences n<60; strictly one-sided; power-of-two seeding
mechanism confirmed in source).
- KNOWN-GAPS gap 14: witness, mechanism, one-sidedness, and the
pinned-pair side condition under which Theorem 3 transfers to the
deployed verifier (pacta's pin-store flow supplies it by
construction). No pacta code change; deployed behavior matches
upstream RFC 9162 implementations.
- fidelity: lied-size family — 73,573 boundary cases, 3,867 expected
divergences PINNED, one-sided direction asserted per case. Banner
rescoped: agreement over pinned families, not extensional equality.
- Theorem3.lean: acceptCons_sound (F2) — soundness over the named
acceptCons predicate, n₀=0 discharged from the non-prefix premise,
size bound derived from acceptance via new consRec_some_le. Cones
read from #print axioms; CONES/AxiomCheck/allowlist updated
(218 → 222 constants, diff = the two theorems + two generated
auxiliaries).
- F3/GPT§7: verification/lean-toolchain pin + run_bare.sh (reviewer's
standalone runner, plain public lean — verified green: 61 cones, 222
constants, gate green) + AENEAS_ENV override in check.sh and
selftest_audit.sh.
- F4: awk field-equality replaces regex-with-dots in Phase 3b.
- F5: git-tracked .pyc removed (worse than reported — it was in the
repo, not just the kit); __pycache__ gitignored; round-4 kit ships a
corpus MANIFEST.sha256 + pinned commit (also GPT's governance
condition).
check.sh exit 0, ATTESTATION GREEN; selftest exit 0, 9/9 + control.
Live LTL untouched (12 leaves, bcd15f9d…); attestation still gated on
ePrint decision + author review + explicit operator order.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Round-2 external reviews (GPT-5.6 + second Claude) converged on the
coverage gate being evadable (H1/NEW-1); GPT additionally proved the
kit's fidelity target could not run (H2) and the namespace-collision
attack that defeats any source-regex fix. This round adopts GPT's
required correction in full:
- Proofs/Inventory.lean: declaration inventory read from the compiled
Lean environment — every constant of every corpus module, fully
qualified, unfiltered (compiler auxiliaries and _private mangles
pinned too), with kind and axiom cone; own cone walker cross-checked
in-process against core collectAxioms (hard error on divergence).
- verification/inventory-allowlist.txt: all 218 constants pinned.
- inventory_gate.sh: fail-closed diff both directions (UNCLASSIFIED /
STALE), INV-COUNT truncation guard, exactly-one-axiom invariant.
- check.sh Phase 3b rewritten around the gate + manifest⇔inventory
drift checks + CONES⇔inventory cone cross-check (two independent
computations must agree). EXCLUDE table gone (sha256/Bytes are
ordinary audited entries now).
- selftest_audit.sh: 9 adversarial cases against the production gate
(attributed/indented/private/instance, namespace collision, smuggled
axiom, deleted decl, unmanifested Proofs/ and gen/ modules) + positive
control — all defeated (GPT release condition 2).
- M1: recursive orphan-olean guard (caught a stray dev artifact on its
first run), gen/ dead-file check, corpus-wide single-axiom pin.
- L1/NEW-2: acceptIncl_sound drops the redundant hm (derived from
hacc.1); cone unchanged.
- M2/M3: STATEMENT-MAP counts 230,271/230,016; non-vacuity guard
wording narrowed to what the guards actually certify.
- README layer table: stale L4/pin-store rows fixed (missed by both
round-2 reviewers AND the round-2 revision — found in self-review).
- KNOWN-GAPS 12 (audit-gate lineage + residual limits), 13 (round-2 kit
target not self-contained); gap 2 count fixed.
- RESPONSE-TO-REVIEWERS.md: round-3 disposition of every finding.
Kit round 3 additionally ships the complete stdlib-only import closure
of pacta.transparency (content-addressed vs pacta 3d81d53), the
clean-extraction fidelity transcript (exit 0, 230,271+230,016, zero
mismatches), the ATTESTATION GREEN check.sh transcript, and the
self-test transcript.
The live LTL remains untouched (12 leaves, root bcd15f9d…);
attestation stays blocked pending ePrint decision + author review +
explicit operator order.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
No theorem was wrong; every fix is spec-surface, audit-mechanism, docs,
or harness coverage. Changes:
LEAN (Claude F1, GPT M4):
- acceptIncl: the consumer's inclusion accept (m<n ∧ Root=some r) is now
a named object, not just a theorem hypothesis. Root alone accepts
out-of-range m; acceptIncl pins the guard.
- acceptIncl_complete / acceptIncl_sound: route Thm 1/2 through it.
- extractCons_correct_paper: Thm 3 at the paper's exact quantifiers
(n₀≤n₁, no separate 0<n₀; n₀=0 discharged since D₀=[]=take 0).
SCRIPT (GPT H1/H2, Claude F3):
- Phase 3b: fail-closed audit-surface COVERAGE — every named decl under
Proofs/ and gen/ must be in CONES or a documented EXCLUDE (sha256,
Bytes); anonymous gen instances count-pinned; every CONES key must be
queried by AxiomCheck (no pin-but-never-check). Tested: an
unclassified theorem now makes the button exit 1.
- H2: distinct markers — LEAN GREEN always, ATTESTATION GREEN only when
fidelity actually ran; SKIP/absent-pacta no longer emit the strong
marker. Attestation gate keys on ATTESTATION GREEN.
- Phase 0: orphan-olean guard (every Proofs/*.olean needs a sibling
.lean); deleted 6 orphans; untracked all *.olean/.lake from git and
gitignored them (root cause of the F3 tarball leak).
HARNESS (Claude F1, GPT M3):
- added out-of-range families (m≥n, m>n, n₀>n₁, n₀=0); re-pinned counts
230,271 / 230,016 (match the reviewer's independent RFC difftest
exactly); narrowed 'exhaustive' wording to the tested domain.
DOCS: README stale rows fixed (freeze banner no longer contradicts
table); KNOWN-GAPS gap 3 reworded (general Lemma 2 = specializations),
+gaps 9 (cost), 10 (pin init), 11 (acceptIncl resolved); STATEMENT-MAP
+acceptIncl rows, +Lemma-2-general note, +constant-vs-property
clarification for §10(i).
Button: EXIT 0, coverage complete, ATTESTATION GREEN, 230,271/230,016.
56 pinned cones over an ENFORCED surface. LTL untouched (12, bcd15f9d).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Audit-of-the-coverage-audit. Its 18 added cone values re-verified against
the observed #print outputs (all match). Methodology blind spots found:
abbrev Bytes (bare alias, no cone content — excluded by nature) and the
two ANONYMOUS gen/ instances, which are silently load-bearing
(DecidableEq Hash powers ConsRec's 'if C = []' and pinAccept's root
compare; Inhabited Hash powers every getD default). Transitivity covered
them, but no hand-waves before external review: cones read and pinned —
instInhabitedHash = [propext], instDecidableEqHash = AXIOM-FREE. The
audit-surface definition is now documented in check.sh itself.
Button verified by exit code: EXIT 0, ALL GREEN, FIDELITY GREEN.
54 pinned cones. LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Re-derived S7 as Fable, practicing the standing rule (check exit code +
ALL GREEN, not tail). Confirmed committed button genuinely exits 0.
FINDING: the cone audit had a COVERAGE gap — 34 of 52 proven objects
were pinned; 18 (incl. core defs kbelow/hleaf/hnode and the pin-store
defs pinAccept/pinExtract/acceptCons, plus intermediate lemmas) were
never cone-audited. Transitively safe (Phase 1 forbids axiom under
Proofs/, Phase 2 forbids sorry, universally) — but 'transitively
covered' is not good enough for an externally-reviewed corpus. Closed:
every proven theorem/def now has its EXACT cone pinned, read from
#print axioms (not guessed). Coverage now 52/52, empty unaudited list.
Cones of note: hleaf/hnode = [LTLAcc.sha256] only; kbelow and the pure
arithmetic/list helpers = no hash axiom; the def-level objects that
touch MTH carry the single sha256 boundary. No surprise axioms anywhere.
Button verified: EXIT 0, ALL GREEN, FIDELITY GREEN, 164,479/164,224
pinned. LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
FIDELITY (the deliverable): fidelity/lean_defs.py transliterates the Lean
MTH/Path/Root/ConsRec (post-refactor decidable-if base) to Python;
fidelity/run_fidelity.py differential-tests them vs the DEPLOYED pacta
verifiers over test_paper_verifiers.py's exact case generation. Result:
MTH==merkle_root (256), Path==inclusion_proof (32,896), verifier
agreement over 164,479 inclusion + 164,224 consistency cases (incl.
honest consistency). Pinned counts match the paper. Wired as check.sh
Phase 4 (gated on pacta presence, SKIP_FIDELITY to skip).
HONEST CORRECTION: three cone pins added in S5.3-S6 were WRONG
(take_all and consRec_base_true_eq are [propext]; consRec_base_false_eq
is [propext, Classical.choice, Quot.sound]) — I had guessed
[propext, Quot.sound]. check.sh's Phase 3 audit was therefore EXITING 1
since S5.3, but I reported 'green' from tailing cert lines instead of
checking the exit code / ALL GREEN. Pins now corrected to the observed
cones; the button now genuinely exits 0 with ALL GREEN + FIDELITY GREEN.
No THEOREM was ever wrong (kernel-checked); the failure was the audit
harness rejecting mis-pinned cones — working as designed, caught late by
my process gap. Process fixed: verify exit code + ALL GREEN, never tail.
35 certs green (verified by exit 0). LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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>
Re-derived S5.3 (all done under an Opus switch) from zero. consRecBinding
STATEMENT re-confirmed faithful to paper Thm 3 steps 1-2 (y=MTH D₁ = the
hash-fold condition; some=>collision / none=>x=MTH(D₁.take n₀) = the two
Lemma-2 outcomes); non-vacuous (some-branch is a SPECIFIC-pair IsCollision,
not pigeonhole-provable; none-branch a real equality needing hcons).
FINDING + FIX: Opus changed ConsRec's base definition (list-match →
decidable if) with only 'recompiled clean' as evidence — a definition
that mirrors the deployed verifier. Now machine-checked: consRec_base_
false_eq / consRec_base_true_eq prove the decidable-if base EQUALS the
exact list-match forms it replaced. Kept as PERMANENT cone-audited
theorems (F1 discipline: keep the evidence), not a throwaway probe.
QUEUED for S5.4: extractCons_correct (Theorem 3 endpoint) MUST carry a
permanent non-vacuity witness like extractIncl_nonvacuous/extractMTH_
nonvacuous. S7 must re-confirm the NEW ConsRec base vs Python.
26 certs green. LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
The single hardest proof in the corpus is complete, no sorry. Under the
value-equality invariant y = MTH D₁, an accepting ConsRec fold either
makes extractConsNode output a genuine collision or its first component
is the honest prefix root MTH(D₁.take n₀).
- ConsRec base changed from list-match to decidable if (if C=[] /
if C.length=1) — same root-cause fix as Root, avoids WF-unfold
exhaustiveness obligations; more faithful to the deployed Python.
Whole chain (Basic..Consistency) rebuilt clean.
- consRecBinding by ConsRec.induct (10 cases): 4 base/singleton, 3
rejection/none contradictions, 2 recursive (n₀≤k, n₀>k). The n₀>k
none-branch is where all S5.1 infrastructure interlocks:
kbelow_prefix_eq (prefix splits at same k) + take_take_le +
take_drop_prefix assemble x = hnode s xx into MTH(D₁.take n₀). The
collision branches use append_inj (fixed-width Hash) + MTH_split.
- take_all helper (take-whole-list).
Cone [propext, Classical.choice, LTLAcc.sha256, Quot.sound] — single hash
axiom. 24 certs green. Fable statement-audit: matches paper Thm 3
steps 1-2. LTL untouched (12 leaves, bcd15f9d).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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 <noreply@anthropic.com>
Theorem 3's binding (steps 1-2) turns on one non-obvious arithmetic fact,
isolated and proven here before the main proof:
- pow2_exp_unique / kbelow_eq_of_pow2_between: kbelow is pinned by its
three defining inequalities (power-of-two, k<n≤2k), so a prefix that
spills past the left subtree splits at the SAME point.
- kbelow_prefix_eq: with k=kbelow n, 2≤n, k<n₀≤n ⇒ kbelow n₀ = k (the
fact the n₀>k recursion branch needs to align MTH(D₁.take n₀) with the
fold).
- take_take_le, take_drop_prefix: the list-surgery identities relating
(D.take n₀) to D.take k and (D.drop k).take (n₀-k).
Cones pinned; 21 certs green. Deliberate honest checkpoint — binding +
extractCons assembly is the next stage. LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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>
Adversarial re-derivation of S3.5 (drill after harness switch). Core
verdict CONFIRMED: extractIncl_correct is faithful and non-vacuous.
Three methodical flaws found and resolved:
- F1: the non-vacuity proof existed only as a deleted probe — evidence
discarded. Now permanent: extractIncl_nonvacuous proves the
extractor's output on a NON-forgery input is NOT a collision, so the
correctness conclusion is false for some inputs and cannot be
discharged by pigeonhole/choice. Guards against future drift back
into vacuity. Cone pinned.
- F2 (queued for S4): deleting root_binding discarded the receipt-
uniqueness content of Lemma 2 (left disjunct: P = Path m D) along
with its vacuous disjunct. To be restored in extractor form during
S4; the S4 consistency walk inlines the same argument regardless.
- F3: README still claimed 'root_binding done' — a deleted theorem
advertised as delivered. Ledger corrected.
15 certs green. LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
The S3 Socratic re-audit found incl_sound was kernel-perfect but VACUOUS:
its '... ∨ HasCollision' disjunct (∃ x y, x≠y ∧ sha256 x = sha256 y) is
provable by pigeonhole ALONE (sha256: infinite List UInt8 → finite
32-byte Hash), so the theorem said nothing about forgeries. Even a
data-carrying {p // IsCollision p} disjunct fails (Classical.choice
inhabits it). The only faithful rendering of the paper's 'explicit
algorithm 𝓔' is a NAMED FUNCTION whose correctness is a claim about ITS
OUTPUT.
- extractIncl (m D d P): total function that walks the honest tree and
returns the concrete colliding preimage pair at the first divergence
(a node preimage pair, or the leaf preimage pair at the bottom).
- extractIncl_correct: d ≠ D[m] ∧ accepting-receipt →
IsCollision (extractIncl …).1 (extractIncl …).2. A statement ABOUT the
fixed function's output; pigeonhole cannot discharge it.
ADVERSARIAL CHECK (probe, since removed): proved
¬ IsCollision (extractIncl 0 [[7]] [7] []) — i.e. on a NON-forgery input
the output is provably NOT a collision, so the conclusion is genuinely
false for some inputs ⇒ non-vacuous, choice-proof.
- Removed the vacuous theorems entirely (incl_sound, root_binding,
hnode/hleaf_inj_or_collision, HasCollision def) so no hollow statement
survives in a corpus destined for the log. Kept the real building
blocks (hnode_preimage_inj [propext]; eq_dropLast helper moved to
Completeness; Binding.lean deleted).
extractIncl_correct cone [propext, Classical.choice, LTLAcc.sha256,
Quot.sound]. THE button green (14 certs). Fable statement-audit passed.
LTL untouched (12 leaves, bcd15f9d).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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>
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 <noreply@anthropic.com>
Path (prover-side inclusion path, paper SS5.3) with termination via the
kbelow bounds; self-contained list lemmas (getD_take, getD_drop - no
stdlib-name dependence); equation lemmas MTH_single/MTH_split/Root_one/
Root_left/Root_right (Option.map form; matcher side conditions closed
explicitly); Theorem 1 by functional induction on Path with a k-fold
discipline against the let-bound split point.
incl_complete cone: [propext, Classical.choice, LTLAcc.sha256,
Quot.sound] - pinned exactly in check.sh alongside Path.
THE button green end to end. LTL untouched.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Accumulator pyramid layers 1-2, mechanizing paper SS5.3/SS6 groundwork:
- gen/LTLAcc/HashExternal.lean: the single sanctioned axiom, opaque
sha256 (no properties assumed - the soundness theorems downstream are
constructive collision extractors).
- Proofs/Basic.lean: hleaf/hnode (0x00/0x01 domain stamps); Lemma 1
(domsep) proven AXIOM-FREE; kbelow (largest power of two below n)
with pos/lt/le-two bound lemmas; MTH, Root (Option = rejection),
ConsRec (four cases, b-flag, pinned anchor) - all with kernel-checked
termination via the kbelow bounds.
- check.sh: estate discipline (stub audit, axiom-smuggling gate,
lean-guard compilation, boundary-exact per-certificate cone audit).
All green; observed cones pinned exactly.
Zero contact with the live LTL: no appends, no server, accumulator
frozen at 12 leaves throughout this project.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
