2026-07-02 12:17:44 +00:00
#!/usr/bin/env bash
# ─────────────────────────────────────────────────────────────────────────────
# check.sh — THE button. Compiles EVERY shipped .lean file and axiom-audits
# EVERY layer certificate. If a file is in this repo, this script checks it;
# if this script doesn't check it, it must not be in the repo.
#
# Phases:
# 0. resource + source-integrity guards
# 1. stub audit: no `by trivial` specs, no True-target theorems, and — the
# anti-axiom-smuggling gate — ZERO `axiom` declarations under Proofs/
# (external models in gen/ are the only sanctioned axiom site)
# 2. compile gen/ + Proofs/ in dependency order (explicit -o, capped cores,
# per-file timeout). Any "declaration uses 'sorry'" warning is a FAILURE
# (this catches sorry robustly — text greps can't, comments mention it).
verification: kernel-side axiom-declaration gate (Phase 2b) + self-test
Phase 1's anti-smuggling check reads source text. Measured today on Lean
v4.30.0-rc2, four distinct declarations compile cleanly and slip past its
anchored pattern:
` axiom cheat : ...` one leading space
`@[simp] axiom cheat : ...` line starts with the attribute
`unsafe axiom cheat : ...` `unsafe` absent from the modifier list
`axiom` <newline> ` cheat` no space follows the keyword
Any of them yields a repository that proves False while the button prints
ALL GREEN. Only the tab variant is blocked, and by Lean, not by us.
Hardening the pattern would fix the exhibited syntax rather than the class,
which is the mistake this estate has made before. Phase 2b stops parsing text
and asks the kernel instead: it reads every compiled Proofs/*.olean with
readModuleData and rejects any declaration that is an axiom.
Design notes:
- reads compiled artifacts rather than importing the modules, because
Proofs.Basic and Proofs.ConstSpecs deliberately reuse `zero_spec` and a
whole-corpus import is impossible by construction;
- membership is self-deriving from the filesystem, so Scalar* and
AxiomCheck are covered too — both are skipped by the CERTS audit and by
the dead-file gate;
- fails closed on absence: a missing .olean would make the scan vacuous, so
the count of compiled modules must equal the count of shipped sources;
- removes its temp source AND artifact on both paths, since a bare `rm`
after the call never runs under `set -e` when the gate goes red — exactly
how this repo accumulated 101 orphan .olean files;
- ~3 s for the whole corpus, against ~53 s for one module-importing run.
Phase 1's grep stays as a fast first line of defence. Phase 2b is the gate
that is load-bearing.
selftest-axgate.sh attacks the shipping gate, lifted out of check.sh at run
time rather than copied. It asserts the specific diagnostic, so a rejection
for an unrelated reason fails too, and it was itself negative-tested: with
the gate's throwError removed, the self-test goes red on exactly that case.
No proof, statement, specification or certificate is touched. No attested
commit is altered — the log binds specific commit hashes, all of which remain
ancestors of HEAD.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-07-28 16:24:18 +00:00
# 2b. kernel-side axiom-declaration gate: read every compiled Proofs/*.olean
# and reject ANY axiom declared there. Phase 1's grep reads source text
# and is evadable four ways (see the phase header); this one asks the
# kernel, derives its scope from the filesystem, and fails closed if the
# set of compiled modules does not match the set of shipped sources.
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# 3. axiom audit: #print axioms for every certificate in CERTS; each must
# report exactly [propext, Classical.choice, Quot.sound]
# ─────────────────────────────────────────────────────────────────────────────
set -euo pipefail
source ~/aeneas-toolchain/env.sh
HERE = " $( cd " $( dirname " $0 " ) " && pwd ) "
AENEAS_LEAN = " $AENEAS_HOME /backends/lean "
TIMEOUT = " ${ LEAN_TIMEOUT :- 300 } "
2026-07-03 10:54:26 +00:00
export LEAN_MEM_MB = " ${ LEAN_MEM_MB :- 8192 } " # 8192: ReduceSpec exceeds 6144 (coherence pass 2)
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CORES = " ${ LEAN_MAX_CORES :- 0 -3 } "
# Layer manifests (extended as the pyramid grows; ORDER = import order).
GEN_MODULES = (
CurveField/TypesExternal
CurveField/Types
CurveField/FunsExternal
CurveField/Funs
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
CurveSig/TypesExternal
CurveSig/Types
CurveSig/FunsExternal
CurveSig/Funs
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)
PROOFS = (
Basic
Denote
P25519
ReduceSpec
SubNegSpec
ConstSpecs
AddSpec
MulSpec
SquareSpec
Square2Spec
Field
InvertSpec
FieldMain
FeQ
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EdCurve
EdDenote
EdDouble
EdAddProjNiels
EdAddAffNiels
EdConvert
EdMain
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DsmTableSpec
DsmStepSpec
DsmLoopSpec
DsmNafLoadSpec
DsmNafMath
NAF encoder proven end-to-end + the phase-1 double-scalar-mul apex
The complete non_adjacent_form(5) verification (four stages):
- `Proofs/DsmNafLoadSpec.lean` (generated) — the LE byte-to-word load.
- `Proofs/DsmNafMath.lean` — the digit loop's arithmetic core: window-read
lemmas (single/cross-word), the exact ZZ invariant steps (Nat.mod_mul
telescope), the carry-kill argument from V < 2^253, and the exit theorem.
- `Proofs/DsmNafLoopSpec.lean` — the w=5 digit loop by induction on the
remaining-bits measure: per-step 64-bit window read (4-way word split),
digit write via hcast/wrapping_sub (exact value window - 32*carry',
oddness, |d| < 16), invariant carried through even/odd steps.
- `Proofs/DsmNafSpec.lean` — the public spec: both entry masserts
DISCHARGED; the digits satisfy the NAF conditions and
sum naf[k]*2^k = V EXACTLY (integers, no modular slack)
for any scalar whose LE byte value V is below 2^253.
And the campaign's brick 4, `Proofs/DsmMulSpec.lean`:
- `run_basepoint` — the transpiled ED25519_BASEPOINT_POINT is the standard
base point: valid extended coordinates (X*Y = Z*T) and the curve equation,
kernel-checked via denominator-free 121666-scaled witnesses. Includes the
generic witness lemmas fp_mul_eq_of_witness / onCurve_of_witness.
- `vartime_double_base_mul_spec` — THE PHASE-1 COMPUTATIONAL SPEC of
vartime_double_base::mul: for canonical scalars and a valid on-curve A,
the result is valid, on-curve, and denotes
dsmFold (naf a) (naf b) (edPt A) edBasePt edId 256
with both digit arrays proven exact NAF encodings. Phase 2 (group
semantics [a]A + [b]B) requires Edwards associativity — deferred and
documented; nothing assumes it.
Also: removed a vestigial pre-re-extraction axiom stub
(backend.serial.scalar_mul.vartime_double_base.mul) from FunsExternal —
a root-level leftover that shadowed the real namespaced definition during
name resolution in proof files. Never referenced by any certificate (the
#print-axioms audit guards against that); deleted for hygiene.
CERTS += naf_load_spec, naf_exit, naf_digit_loop_spec,
non_adjacent_form_spec, run_basepoint, vartime_double_base_mul_spec —
each audited to exactly [propext, Classical.choice, Quot.sound].
Full check.sh green.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 14:52:06 +00:00
DsmNafLoopSpec
DsmNafSpec
DsmMulSpec
Phase 2, brick 1a: to_bytes canonicity proven (to_bytes_spec, kernel-audited)
The load-bearing brick of the point-level apex equation:
FieldElement51::to_bytes always succeeds and its 32 output bytes denote
EXACTLY the represented residue - bytesVal s = feVal a mod p. Since the
canonical residue determines the bytes, this is simultaneously
canonicity ("output is the canonical encoding") and the injectivity
compress needs ("equal residues iff equal bytes").
- Proofs/ToBytesMath.lean: the context-free ℕ mathematics (METHOD 4) -
the 5-rung carry telescope (div_rung/q_telescope), the q-trick facts
(q = (h+19)/2^255 is a bit, fires iff h >= p), q_mod_p (adding 19q and
discarding bit 255 subtracts pq exactly), carry_pack (the masked-limb
assembly mod 2^255), five per-limb byte-chunk splits, and bytes_pack
(the 32-byte little-endian reassembly, closed by one zify +
linear_combination over the five splits).
- Proofs/ToBytesSpec.lean: the symbolic execution - at ~150 machine ops
the longest walk in the repo, loop-free: weak reduce (reduce_spec),
the q pass, the fold + carry pass, 32 byte extractions (the four
limb-boundary bytes turn disjoint ORs into additions via
Nat.two_pow_add_eq_or_of_lt), and the trailing top-bit debug-assert
DISCHARGED (b31 = f4/2^44 < 2^7), not assumed.
- check.sh: ToBytesMath/ToBytesSpec in PROOFS, to_bytes_spec in CERTS
(exact standard-three audit) - full button green fresh.
Walk lessons (for the control repo, next push): rw index-equations into
their consumers instead of subst (subst eliminates the wrong side or
dies on dependent do-motives); never rw [Nat.mod_eq_of_lt (by omega)]
(metavariable goal reaches omega) - state the bound with show.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 11:10:43 +00:00
ToBytesMath
ToBytesSpec
Phase 2, brick 1 complete: ed_compress_spec - compress emits the canonical
encoding of the denoted affine point (kernel-audited)
CurveFieldProofs.ed_compress_spec: for any valid extended point Pt
(ExtValid - the invariant every certified curve op guarantees),
compress Pt = ok s with
bytesVal s = (edY Pt).val + ((edX Pt).val % 2) * 2^255
- the 32 wire bytes are the canonical little-endian y-residue with the
x-parity bit at position 255. Compress semantics AND canonicity in one
statement, because to_bytes_spec pins the bytes to the residue itself.
Supporting certificates in Proofs/CompressSpec.lean:
- is_negative_spec: the sign read is the parity of the CANONICAL residue
(bit 0 of to_bytes) - (feVal x mod p) mod 2.
- Bytes32.exists_bytes: the 32-byte destructuring device (the
Fe.exists_limbs idiom, 32-wide).
- to_bytes_spec': premise-free restatement of the canonicity brick.
- xor_top_bit (ToBytesMath): setting a clear top bit by XOR is addition -
proven from xor_div_two_pow + and_xor_distrib_right, no bit-blasting.
The chain is entirely certified code: invert (Fermat), two muls, to_bytes
(canonicity), is_negative, and the sign-bit XOR. Axiom cone of
ed_compress_spec: exactly [propext, Classical.choice, Quot.sound].
check.sh: CompressSpec in PROOFS, ed_compress_spec in CERTS - full button
green fresh.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 11:33:58 +00:00
CompressSpec
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ScalarPackSpec
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
SigApexSpec
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PointLiftSpec
2026-07-05 16:27:25 +00:00
PointEqSpec
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DecompressSpec
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FromBytesSpec
PHASE 2 COMPLETE ON DALEK: THE FULL POINT-LEVEL LIFT
(verify_accepts_iff_decompress, button-enforced)
THE THEOREM: under the apex hypotheses, the signature's R bytes
DECOMPRESS to a valid on-curve point Pt, and
verifier accepts <=> Pt = [k]*(-A) + [s]*B (as points)
- accept iff decompress(R) equals the recomputed point. Every link of
the chain (byte comparison <-> canonical-encoding equality <-> point
equality <-> decompressed-point equality) is machine-checked over the
extracted code. Axiom cone EXACTLY the SHA-512 + wire-format boundary;
Phase 3b now enforces FOUR certificate tiers (byte apex, half-lift,
point equation, full lift).
Proofs/DecompressMain.lean:
- edwards_d_denote: the extracted EDWARDS_D constant denotes THE curve
d (edwards_d_spec + edD_char cancelled by 121666 nonzero).
- decompress_of_canonical (standard three axioms): canonical encodings
of valid on-curve points decompress to them - from_bytes recovers the
y-residue exactly (sign bit discarded), Q's own x witnesses the
square so sqrt_ratio_i returns the even root, the sign bit (Q's
x-parity, from byte 31) selects +/-root, and the parity-injectivity
argument pins the selection to edX Q; the assembled {X,Y,1,X*Y} is
ExtValid and on-curve.
- verify_accepts_iff_decompress: the capstone composition.
Full button green fresh. Remaining: replicate x3, coherence pass 4.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 22:05:55 +00:00
DecompressMain
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)
# Fully-qualified certificate names; each must be axiom-clean.
CERTS = (
CurveFieldProofs.fieldImplementation
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CurveFieldProofs.edwardsImplementation
2026-07-04 13:30:18 +00:00
CurveFieldProofs.naf_table_spec
CurveFieldProofs.naf_select_spec
CurveFieldProofs.proj_double_law
CurveFieldProofs.compl_as_projective_law
CurveFieldProofs.dsm_step_p_law
CurveFieldProofs.dsm_step_b_law
CurveFieldProofs.dsm_loop_spec
CurveFieldProofs.naf_load_spec
CurveFieldProofs.naf_exit
NAF encoder proven end-to-end + the phase-1 double-scalar-mul apex
The complete non_adjacent_form(5) verification (four stages):
- `Proofs/DsmNafLoadSpec.lean` (generated) — the LE byte-to-word load.
- `Proofs/DsmNafMath.lean` — the digit loop's arithmetic core: window-read
lemmas (single/cross-word), the exact ZZ invariant steps (Nat.mod_mul
telescope), the carry-kill argument from V < 2^253, and the exit theorem.
- `Proofs/DsmNafLoopSpec.lean` — the w=5 digit loop by induction on the
remaining-bits measure: per-step 64-bit window read (4-way word split),
digit write via hcast/wrapping_sub (exact value window - 32*carry',
oddness, |d| < 16), invariant carried through even/odd steps.
- `Proofs/DsmNafSpec.lean` — the public spec: both entry masserts
DISCHARGED; the digits satisfy the NAF conditions and
sum naf[k]*2^k = V EXACTLY (integers, no modular slack)
for any scalar whose LE byte value V is below 2^253.
And the campaign's brick 4, `Proofs/DsmMulSpec.lean`:
- `run_basepoint` — the transpiled ED25519_BASEPOINT_POINT is the standard
base point: valid extended coordinates (X*Y = Z*T) and the curve equation,
kernel-checked via denominator-free 121666-scaled witnesses. Includes the
generic witness lemmas fp_mul_eq_of_witness / onCurve_of_witness.
- `vartime_double_base_mul_spec` — THE PHASE-1 COMPUTATIONAL SPEC of
vartime_double_base::mul: for canonical scalars and a valid on-curve A,
the result is valid, on-curve, and denotes
dsmFold (naf a) (naf b) (edPt A) edBasePt edId 256
with both digit arrays proven exact NAF encodings. Phase 2 (group
semantics [a]A + [b]B) requires Edwards associativity — deferred and
documented; nothing assumes it.
Also: removed a vestigial pre-re-extraction axiom stub
(backend.serial.scalar_mul.vartime_double_base.mul) from FunsExternal —
a root-level leftover that shadowed the real namespaced definition during
name resolution in proof files. Never referenced by any certificate (the
#print-axioms audit guards against that); deleted for hygiene.
CERTS += naf_load_spec, naf_exit, naf_digit_loop_spec,
non_adjacent_form_spec, run_basepoint, vartime_double_base_mul_spec —
each audited to exactly [propext, Classical.choice, Quot.sound].
Full check.sh green.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 14:52:06 +00:00
CurveFieldProofs.naf_digit_loop_spec
CurveFieldProofs.non_adjacent_form_spec
CurveFieldProofs.run_basepoint
CurveFieldProofs.vartime_double_base_mul_spec
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
CurveFieldProofs.verify_loop_full
Phase 2, brick 1a: to_bytes canonicity proven (to_bytes_spec, kernel-audited)
The load-bearing brick of the point-level apex equation:
FieldElement51::to_bytes always succeeds and its 32 output bytes denote
EXACTLY the represented residue - bytesVal s = feVal a mod p. Since the
canonical residue determines the bytes, this is simultaneously
canonicity ("output is the canonical encoding") and the injectivity
compress needs ("equal residues iff equal bytes").
- Proofs/ToBytesMath.lean: the context-free ℕ mathematics (METHOD 4) -
the 5-rung carry telescope (div_rung/q_telescope), the q-trick facts
(q = (h+19)/2^255 is a bit, fires iff h >= p), q_mod_p (adding 19q and
discarding bit 255 subtracts pq exactly), carry_pack (the masked-limb
assembly mod 2^255), five per-limb byte-chunk splits, and bytes_pack
(the 32-byte little-endian reassembly, closed by one zify +
linear_combination over the five splits).
- Proofs/ToBytesSpec.lean: the symbolic execution - at ~150 machine ops
the longest walk in the repo, loop-free: weak reduce (reduce_spec),
the q pass, the fold + carry pass, 32 byte extractions (the four
limb-boundary bytes turn disjoint ORs into additions via
Nat.two_pow_add_eq_or_of_lt), and the trailing top-bit debug-assert
DISCHARGED (b31 = f4/2^44 < 2^7), not assumed.
- check.sh: ToBytesMath/ToBytesSpec in PROOFS, to_bytes_spec in CERTS
(exact standard-three audit) - full button green fresh.
Walk lessons (for the control repo, next push): rw index-equations into
their consumers instead of subst (subst eliminates the wrong side or
dies on dependent do-motives); never rw [Nat.mod_eq_of_lt (by omega)]
(metavariable goal reaches omega) - state the bound with show.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 11:10:43 +00:00
CurveFieldProofs.to_bytes_spec
Phase 2, brick 1 complete: ed_compress_spec - compress emits the canonical
encoding of the denoted affine point (kernel-audited)
CurveFieldProofs.ed_compress_spec: for any valid extended point Pt
(ExtValid - the invariant every certified curve op guarantees),
compress Pt = ok s with
bytesVal s = (edY Pt).val + ((edX Pt).val % 2) * 2^255
- the 32 wire bytes are the canonical little-endian y-residue with the
x-parity bit at position 255. Compress semantics AND canonicity in one
statement, because to_bytes_spec pins the bytes to the residue itself.
Supporting certificates in Proofs/CompressSpec.lean:
- is_negative_spec: the sign read is the parity of the CANONICAL residue
(bit 0 of to_bytes) - (feVal x mod p) mod 2.
- Bytes32.exists_bytes: the 32-byte destructuring device (the
Fe.exists_limbs idiom, 32-wide).
- to_bytes_spec': premise-free restatement of the canonicity brick.
- xor_top_bit (ToBytesMath): setting a clear top bit by XOR is addition -
proven from xor_div_two_pow + and_xor_distrib_right, no bit-blasting.
The chain is entirely certified code: invert (Fermat), two muls, to_bytes
(canonicity), is_negative, and the sign-bit XOR. Axiom cone of
ed_compress_spec: exactly [propext, Classical.choice, Quot.sound].
check.sh: CompressSpec in PROOFS, ed_compress_spec in CERTS - full button
green fresh.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 11:33:58 +00:00
CurveFieldProofs.ed_compress_spec
2026-07-05 12:10:09 +00:00
ScalarProofs.from_bytes_mod_order_wide_spec
2026-07-05 12:36:03 +00:00
CurveFieldProofs.vartime_dsm_basepoint_spec
2026-07-05 16:27:25 +00:00
CurveFieldProofs.enc_point_inj
2026-07-05 18:08:21 +00:00
CurveFieldProofs.pow_p58_spec
CurveFieldProofs.fe_ct_eq_spec
2026-07-05 19:16:05 +00:00
CurveFieldProofs.sqrt_core
Phase 2, decompress part 2b: THE SQUARE-ROOT WALK PROVEN
(sqrt_ratio_i_sq_spec, kernel-audited)
The largest single proof of the decompress chain: for square u/v
(witness x, v nonzero), the extracted sqrt_ratio_i returns choice 1 and
the even-parity root - Bnd r (2^52), r^2 * v = u, r's canonical residue
even. The walk composes every previously certified piece: the
square/mul/pow_p58 candidate chain, sqrt_m1_spec, fe_ct_eq_spec x3 (the
three constant-time residue checks), neg_spec, the Choice bitor, and
fe_cond_assign_spec twice (root flip by sqrt(-1), then sign
normalization via is_negative).
Case analysis: sqrt_core's disjunction (v*r^2 = +/-u) against the check
flags - u = 0 collapses everything to the zero root; u != 0 with
v*r^2 = u kills both flip flags (u = -u forces u = 0 in odd
characteristic; u = -u*i forces u*(1+i) = 0 with 1+i nonzero); with
v*r^2 = -u the flip fires and (i*r)^2 * v = -(-u) = u. Parity: the odd-
prime negation flip (ZMod.neg_val), zero-root edge included. New
helpers: eq_neg_self_iff_zero, one_add_i_ne_zero.
Certificate exact standard three; full button green fresh. Remaining:
from_bytes walk, decompress_of_canonical, replication, pass 4.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 20:03:57 +00:00
CurveFieldProofs.sqrt_ratio_i_sq_spec
2026-07-05 20:55:18 +00:00
CurveFieldProofs.from_bytes_spec
PHASE 2 COMPLETE ON DALEK: THE FULL POINT-LEVEL LIFT
(verify_accepts_iff_decompress, button-enforced)
THE THEOREM: under the apex hypotheses, the signature's R bytes
DECOMPRESS to a valid on-curve point Pt, and
verifier accepts <=> Pt = [k]*(-A) + [s]*B (as points)
- accept iff decompress(R) equals the recomputed point. Every link of
the chain (byte comparison <-> canonical-encoding equality <-> point
equality <-> decompressed-point equality) is machine-checked over the
extracted code. Axiom cone EXACTLY the SHA-512 + wire-format boundary;
Phase 3b now enforces FOUR certificate tiers (byte apex, half-lift,
point equation, full lift).
Proofs/DecompressMain.lean:
- edwards_d_denote: the extracted EDWARDS_D constant denotes THE curve
d (edwards_d_spec + edD_char cancelled by 121666 nonzero).
- decompress_of_canonical (standard three axioms): canonical encodings
of valid on-curve points decompress to them - from_bytes recovers the
y-residue exactly (sign bit discarded), Q's own x witnesses the
square so sqrt_ratio_i returns the even root, the sign bit (Q's
x-parity, from byte 31) selects +/-root, and the parity-injectivity
argument pins the selection to edX Q; the assembled {X,Y,1,X*Y} is
ExtValid and on-curve.
- verify_accepts_iff_decompress: the capstone composition.
Full button green fresh. Remaining: replicate x3, coherence pass 4.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 22:05:55 +00:00
CurveFieldProofs.decompress_of_canonical
2026-07-02 12:17:44 +00:00
)
# Imports needed so every certificate in CERTS is in scope for the audit.
AUDIT_IMPORTS = (
Proofs.FieldMain
2026-07-02 12:50:42 +00:00
Proofs.EdMain
2026-07-04 13:30:18 +00:00
Proofs.DsmTableSpec
Proofs.DsmStepSpec
Proofs.DsmLoopSpec
Proofs.DsmNafLoadSpec
Proofs.DsmNafMath
NAF encoder proven end-to-end + the phase-1 double-scalar-mul apex
The complete non_adjacent_form(5) verification (four stages):
- `Proofs/DsmNafLoadSpec.lean` (generated) — the LE byte-to-word load.
- `Proofs/DsmNafMath.lean` — the digit loop's arithmetic core: window-read
lemmas (single/cross-word), the exact ZZ invariant steps (Nat.mod_mul
telescope), the carry-kill argument from V < 2^253, and the exit theorem.
- `Proofs/DsmNafLoopSpec.lean` — the w=5 digit loop by induction on the
remaining-bits measure: per-step 64-bit window read (4-way word split),
digit write via hcast/wrapping_sub (exact value window - 32*carry',
oddness, |d| < 16), invariant carried through even/odd steps.
- `Proofs/DsmNafSpec.lean` — the public spec: both entry masserts
DISCHARGED; the digits satisfy the NAF conditions and
sum naf[k]*2^k = V EXACTLY (integers, no modular slack)
for any scalar whose LE byte value V is below 2^253.
And the campaign's brick 4, `Proofs/DsmMulSpec.lean`:
- `run_basepoint` — the transpiled ED25519_BASEPOINT_POINT is the standard
base point: valid extended coordinates (X*Y = Z*T) and the curve equation,
kernel-checked via denominator-free 121666-scaled witnesses. Includes the
generic witness lemmas fp_mul_eq_of_witness / onCurve_of_witness.
- `vartime_double_base_mul_spec` — THE PHASE-1 COMPUTATIONAL SPEC of
vartime_double_base::mul: for canonical scalars and a valid on-curve A,
the result is valid, on-curve, and denotes
dsmFold (naf a) (naf b) (edPt A) edBasePt edId 256
with both digit arrays proven exact NAF encodings. Phase 2 (group
semantics [a]A + [b]B) requires Edwards associativity — deferred and
documented; nothing assumes it.
Also: removed a vestigial pre-re-extraction axiom stub
(backend.serial.scalar_mul.vartime_double_base.mul) from FunsExternal —
a root-level leftover that shadowed the real namespaced definition during
name resolution in proof files. Never referenced by any certificate (the
#print-axioms audit guards against that); deleted for hygiene.
CERTS += naf_load_spec, naf_exit, naf_digit_loop_spec,
non_adjacent_form_spec, run_basepoint, vartime_double_base_mul_spec —
each audited to exactly [propext, Classical.choice, Quot.sound].
Full check.sh green.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 14:52:06 +00:00
Proofs.DsmNafSpec
Proofs.DsmMulSpec
Phase 2, brick 1a: to_bytes canonicity proven (to_bytes_spec, kernel-audited)
The load-bearing brick of the point-level apex equation:
FieldElement51::to_bytes always succeeds and its 32 output bytes denote
EXACTLY the represented residue - bytesVal s = feVal a mod p. Since the
canonical residue determines the bytes, this is simultaneously
canonicity ("output is the canonical encoding") and the injectivity
compress needs ("equal residues iff equal bytes").
- Proofs/ToBytesMath.lean: the context-free ℕ mathematics (METHOD 4) -
the 5-rung carry telescope (div_rung/q_telescope), the q-trick facts
(q = (h+19)/2^255 is a bit, fires iff h >= p), q_mod_p (adding 19q and
discarding bit 255 subtracts pq exactly), carry_pack (the masked-limb
assembly mod 2^255), five per-limb byte-chunk splits, and bytes_pack
(the 32-byte little-endian reassembly, closed by one zify +
linear_combination over the five splits).
- Proofs/ToBytesSpec.lean: the symbolic execution - at ~150 machine ops
the longest walk in the repo, loop-free: weak reduce (reduce_spec),
the q pass, the fold + carry pass, 32 byte extractions (the four
limb-boundary bytes turn disjoint ORs into additions via
Nat.two_pow_add_eq_or_of_lt), and the trailing top-bit debug-assert
DISCHARGED (b31 = f4/2^44 < 2^7), not assumed.
- check.sh: ToBytesMath/ToBytesSpec in PROOFS, to_bytes_spec in CERTS
(exact standard-three audit) - full button green fresh.
Walk lessons (for the control repo, next push): rw index-equations into
their consumers instead of subst (subst eliminates the wrong side or
dies on dependent do-motives); never rw [Nat.mod_eq_of_lt (by omega)]
(metavariable goal reaches omega) - state the bound with show.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 11:10:43 +00:00
Proofs.ToBytesSpec
Phase 2, brick 1 complete: ed_compress_spec - compress emits the canonical
encoding of the denoted affine point (kernel-audited)
CurveFieldProofs.ed_compress_spec: for any valid extended point Pt
(ExtValid - the invariant every certified curve op guarantees),
compress Pt = ok s with
bytesVal s = (edY Pt).val + ((edX Pt).val % 2) * 2^255
- the 32 wire bytes are the canonical little-endian y-residue with the
x-parity bit at position 255. Compress semantics AND canonicity in one
statement, because to_bytes_spec pins the bytes to the residue itself.
Supporting certificates in Proofs/CompressSpec.lean:
- is_negative_spec: the sign read is the parity of the CANONICAL residue
(bit 0 of to_bytes) - (feVal x mod p) mod 2.
- Bytes32.exists_bytes: the 32-byte destructuring device (the
Fe.exists_limbs idiom, 32-wide).
- to_bytes_spec': premise-free restatement of the canonicity brick.
- xor_top_bit (ToBytesMath): setting a clear top bit by XOR is addition -
proven from xor_div_two_pow + and_xor_distrib_right, no bit-blasting.
The chain is entirely certified code: invert (Fermat), two muls, to_bytes
(canonicity), is_negative, and the sign-bit XOR. Axiom cone of
ed_compress_spec: exactly [propext, Classical.choice, Quot.sound].
check.sh: CompressSpec in PROOFS, ed_compress_spec in CERTS - full button
green fresh.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 11:33:58 +00:00
Proofs.CompressSpec
2026-07-05 12:10:09 +00:00
Proofs.ScalarPackSpec
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
Proofs.SigApexSpec
2026-07-05 12:36:03 +00:00
Proofs.PointLiftSpec
2026-07-05 16:27:25 +00:00
Proofs.PointEqSpec
2026-07-05 18:08:21 +00:00
Proofs.DecompressSpec
2026-07-05 20:55:18 +00:00
Proofs.FromBytesSpec
PHASE 2 COMPLETE ON DALEK: THE FULL POINT-LEVEL LIFT
(verify_accepts_iff_decompress, button-enforced)
THE THEOREM: under the apex hypotheses, the signature's R bytes
DECOMPRESS to a valid on-curve point Pt, and
verifier accepts <=> Pt = [k]*(-A) + [s]*B (as points)
- accept iff decompress(R) equals the recomputed point. Every link of
the chain (byte comparison <-> canonical-encoding equality <-> point
equality <-> decompressed-point equality) is machine-checked over the
extracted code. Axiom cone EXACTLY the SHA-512 + wire-format boundary;
Phase 3b now enforces FOUR certificate tiers (byte apex, half-lift,
point equation, full lift).
Proofs/DecompressMain.lean:
- edwards_d_denote: the extracted EDWARDS_D constant denotes THE curve
d (edwards_d_spec + edD_char cancelled by 121666 nonzero).
- decompress_of_canonical (standard three axioms): canonical encodings
of valid on-curve points decompress to them - from_bytes recovers the
y-residue exactly (sign bit discarded), Q's own x witnesses the
square so sqrt_ratio_i returns the even root, the sign bit (Q's
x-parity, from byte 31) selects +/-root, and the parity-injectivity
argument pins the selection to edX Q; the assembled {X,Y,1,X*Y} is
ExtValid and on-curve.
- verify_accepts_iff_decompress: the capstone composition.
Full button green fresh. Remaining: replicate x3, coherence pass 4.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 22:05:55 +00:00
Proofs.DecompressMain
2026-07-02 12:17:44 +00:00
)
# ── Phase 0: resource + integrity guards ────────────────────────────────────
free -m | awk '/Mem:/{if($7<2048){print "FATAL: <2GB RAM available — refusing to compile"; exit 1}}'
echo "=== Phase 0: source integrity ==="
for f in " $HERE " /gen/CurveField/*.lean " $HERE " /Proofs/*.lean; do
[ -f " $f " ] || continue
if ! grep -qE '^(/-|import |namespace |theorem |def |open |set_option |--)' " $f " ; then
echo " CORRUPTED: $f is not Lean source (olean clobber?). Restore: git checkout HEAD -- $f "
exit 1
fi
done
echo " all sources valid"
# ── Phase 1: stub + axiom-smuggling audit ───────────────────────────────────
echo "=== Phase 1: stub audit ==="
if grep -rn 'by trivial' " $HERE " /Proofs/*Spec*.lean 2>/dev/null; then
echo "STUB DETECTED: 'by trivial' in spec files" ; exit 1; fi
if grep -rn ' : True :=' " $HERE " /Proofs/*.lean 2>/dev/null; then
echo "STUB DETECTED: True-target theorem" ; exit 1; fi
if grep -rnE '^(private |protected |noncomputable )*axiom ' " $HERE " /Proofs/*.lean 2>/dev/null; then
echo "AXIOM SMUGGLING DETECTED: axiom declaration under Proofs/ — forbidden."
echo "External models belong in gen/*/FunsExternal.lean and must stay outside"
echo "every certificate's dependency cone (Phase 3 verifies that)."
exit 1
fi
echo " clean: no trivial stubs, no True targets, no axioms outside gen/"
# ── Phase 2: compile everything shipped ─────────────────────────────────────
echo "=== Phase 2: compile ==="
LOG = $( mktemp /tmp/check-compile-XXXX.log)
cd " $AENEAS_LEAN "
lake env bash -c "
set -euo pipefail
cd '$HERE/gen' && export LEAN_PATH = \" \$ LEAN_PATH:\$ PWD:$HERE \"
compile( ) {
echo \" · \$ 1\"
2026-07-02 14:10:55 +00:00
LEAN_TIMEOUT = $TIMEOUT LEAN_MAX_CORES = $CORES '$HERE/lean-guard' \" \$ { 1} .lean\" 2>& 1 | tee -a '$LOG' || { echo \" FAIL: \$ 1\" ; exit 1; }
2026-07-02 12:17:44 +00:00
}
for m in ${ GEN_MODULES [*] } ; do compile \" \$ m\" ; done
cd '$HERE'
for m in ${ PROOFS [*] } ; do
[ -f \" Proofs/\$ m.lean\" ] || { echo \" MISSING: Proofs/\$ m.lean listed in manifest\" ; exit 1; }
compile \" Proofs/\$ m\"
done
# every shipped proof file must be in the manifest (no dead files)
for f in Proofs/*.lean; do
b = \$ ( basename \" \$ f\" .lean)
[ \" \$ b\" = AxiomCheck ] && continue
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case \" \$ b\" in Scalar*) continue ; ; esac # scalar layer: checked by check-scalar.sh (coherence pass 2)
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case \" ${ PROOFS [*] } \" in ( *\" \$ b \" *) ; ; ( *) echo \" DEAD FILE: \$ f not in check manifest\" ; exit 1; ; esac
done
"
if grep -q "uses 'sorry'" " $LOG " ; then
echo "STUB DETECTED: a compiled declaration uses 'sorry'" ; exit 1; fi
rm -f " $LOG "
verification: kernel-side axiom-declaration gate (Phase 2b) + self-test
Phase 1's anti-smuggling check reads source text. Measured today on Lean
v4.30.0-rc2, four distinct declarations compile cleanly and slip past its
anchored pattern:
` axiom cheat : ...` one leading space
`@[simp] axiom cheat : ...` line starts with the attribute
`unsafe axiom cheat : ...` `unsafe` absent from the modifier list
`axiom` <newline> ` cheat` no space follows the keyword
Any of them yields a repository that proves False while the button prints
ALL GREEN. Only the tab variant is blocked, and by Lean, not by us.
Hardening the pattern would fix the exhibited syntax rather than the class,
which is the mistake this estate has made before. Phase 2b stops parsing text
and asks the kernel instead: it reads every compiled Proofs/*.olean with
readModuleData and rejects any declaration that is an axiom.
Design notes:
- reads compiled artifacts rather than importing the modules, because
Proofs.Basic and Proofs.ConstSpecs deliberately reuse `zero_spec` and a
whole-corpus import is impossible by construction;
- membership is self-deriving from the filesystem, so Scalar* and
AxiomCheck are covered too — both are skipped by the CERTS audit and by
the dead-file gate;
- fails closed on absence: a missing .olean would make the scan vacuous, so
the count of compiled modules must equal the count of shipped sources;
- removes its temp source AND artifact on both paths, since a bare `rm`
after the call never runs under `set -e` when the gate goes red — exactly
how this repo accumulated 101 orphan .olean files;
- ~3 s for the whole corpus, against ~53 s for one module-importing run.
Phase 1's grep stays as a fast first line of defence. Phase 2b is the gate
that is load-bearing.
selftest-axgate.sh attacks the shipping gate, lifted out of check.sh at run
time rather than copied. It asserts the specific diagnostic, so a rejection
for an unrelated reason fails too, and it was itself negative-tested: with
the gate's throwError removed, the self-test goes red on exactly that case.
No proof, statement, specification or certificate is touched. No attested
commit is altered — the log binds specific commit hashes, all of which remain
ancestors of HEAD.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-07-28 16:24:18 +00:00
# ── Phase 2b: kernel-side axiom-declaration gate ────────────────────────────
# WHY THIS EXISTS. Phase 1's anti-smuggling check reads SOURCE TEXT, and a
# source-text grep is the wrong instrument. Measured on Lean v4.30.0-rc2
# (2026-07-28), each of the following compiles cleanly and slips past it:
# ` axiom cheat : ...` (one leading space — the pattern is anchored)
# `@[simp] axiom cheat : ...` (line starts with the attribute)
# `unsafe axiom cheat : ...` (`unsafe` is not in the modifier alternation)
# `axiom` <newline> ` cheat` (no space follows the keyword)
# Only the tab variant is blocked, and by Lean itself, not by us. Hardening the
# pattern would fix the exhibited syntax rather than the class; the class fix is
# to stop parsing text and ask the kernel, which is what this phase does.
# Ported from fips205-slhdsa-verified/verification/Proofs/Audit.lean.
#
# Phase 1's grep is kept as a fast, readable first line of defence. THIS is the
# gate that is load-bearing.
echo "=== Phase 2b: kernel-side axiom-declaration gate ==="
# dot-prefixed and inside $HERE: `lean` refuses a file outside the root
# directory, and a leading dot keeps it out of every *.lean glob.
# The gate reads the COMPILED ARTIFACTS directly (readModuleData) rather than
# importing the modules. Two reasons, both load-bearing:
# · Proofs.Basic and Proofs.ConstSpecs deliberately reuse the name
# `zero_spec` (they are never imported together), so a whole-corpus import
# is impossible by construction — it fails with "environment already
# contains". Reading oleans merges nothing, so collisions cannot arise.
# · Membership is then SELF-DERIVING from the filesystem: every .olean under
# Proofs/ is scanned, including Scalar* and AxiomCheck, which the CERTS
# audit and the dead-file gate both skip. Nothing is on a hand-kept list.
# Cost is ~3 s for the whole corpus (no mathlib import), against ~53 s for a
# single module-importing invocation.
N_PROOF_SRC = $( ls -1 " $HERE " /Proofs/*.lean 2>/dev/null | wc -l)
GATE = $( mktemp " $HERE /.axgate-XXXX.lean " )
{
echo "import Lean"
echo "open Lean"
echo " def expectedModules : Nat := $N_PROOF_SRC "
cat <<'LEANGATE'
run_cmd do
let dir : System.FilePath := "Proofs"
let mut errs : Array String := #[]
let mut nMod := 0
let mut nConst := 0
for entry in ( ← dir.readDir) do
if entry.path.extension = = some "olean" then
nMod := nMod + 1
let ( mod, _) ← readModuleData entry.path
for ci in mod.constants do
nConst := nConst + 1
if ci matches .axiomInfo _ then
errs := errs.push s!" {entry.fileName}: {ci.name}"
unless errs.isEmpty do
throwError "AXIOM DECLARED under Proofs/ (kernel-side gate):\n{String.intercalate " \n " errs.toList}"
-- FAIL CLOSED ON ABSENCE: an empty result and a clean result must not share
-- a code path. A deleted .olean would make the scan above vacuous; an extra
-- one is orphan litter with no shipped source.
if nMod != expectedModules then
throwError "COVERAGE MISMATCH under Proofs/: scanned {nMod} compiled modules, but the directory ships {expectedModules} sources. A missing .olean makes this gate vacuous; an extra .olean is an orphan with no source."
logInfo s!" kernel confirms: {nConst} declarations across {nMod} compiled Proofs modules, none is an axiom"
LEANGATE
} > " $GATE "
cd " $AENEAS_LEAN "
# The temp source AND its compiled artifact are removed on BOTH paths. Under
# `set -e` a bare `rm` after the call never runs when the gate goes red, which
# is exactly how this repo accumulated 101 orphan .olean files (fixed today).
GATE_RC = 0
lake env bash -c "
set -euo pipefail
cd '$HERE/gen' && export LEAN_PATH = \" \$ LEAN_PATH:\$ PWD:$HERE \"
cd '$HERE'
LEAN_TIMEOUT = $TIMEOUT LEAN_MAX_CORES = $CORES '$HERE/lean-guard' '$GATE'
" || GATE_RC= $?
rm -f " $GATE " " ${ GATE %.lean } .olean "
if [ " $GATE_RC " -ne 0 ] ; then
echo "AXIOM SMUGGLING GATE FAILED (kernel-side) — see the error above."
exit 1
fi
2026-07-02 12:17:44 +00:00
# ── Phase 3: axiom audit of every certificate ───────────────────────────────
echo "=== Phase 3: axiom audit ==="
EXPECTED = "[propext, Classical.choice, Quot.sound]"
cd " $AENEAS_LEAN "
lake env bash -c "
set -euo pipefail
cd '$HERE/gen' && export LEAN_PATH = \" \$ LEAN_PATH:\$ PWD:$HERE \"
cd '$HERE'
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AUD = \$ ( mktemp '$HERE/.audit-XXXX.lean' )
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{
for i in ${ AUDIT_IMPORTS [*] } ; do echo \" import \$ i\" ; done
for c in ${ CERTS [*] } ; do echo \" #print axioms \$c\"; done
} > \" \$ AUD\"
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OUT = \$ ( LEAN_TIMEOUT = $TIMEOUT LEAN_MEM_MB = 4096 '$HERE/lean-guard' \" \$ AUD\" 2>& 1)
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echo \" \$ OUT\"
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rm -f \" \$ AUD\" \" \$ { AUD%.lean} .olean\"
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N_CLEAN = \$ ( echo \" \$ OUT\" | grep -cF \" depends on axioms: $EXPECTED \" || true )
if [ \" \$ N_CLEAN\" -ne ${# CERTS [@] } ] ; then
echo \" AXIOM AUDIT FAILED: \$ N_CLEAN/${# CERTS [@] } certificates clean\"
exit 1
fi
"
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
echo ""
echo "=== Phase 3b: signature-apex audit (SHA-512 + wire-format boundary) ==="
# The verification-equation apex is grounded in the PROVEN curve model; its
# only axioms beyond the standard three are the deliberate, documented
# boundary: the SHA-512 hash oracle and the opaque wire-format types.
# NO curve axioms, NO scalar axioms, NO backend-dispatch axioms.
cd " $AENEAS_LEAN "
lake env bash -c "
set -euo pipefail
cd '$HERE/gen' && export LEAN_PATH = \" \$ LEAN_PATH:\$ PWD:$HERE \"
cd '$HERE'
ALLOWED = '[propext, Classical.choice, Quot.sound, ed25519.Signature, sha2.Sha512, verifying.sha512_finalize_bytes, verifying.sha512_new, verifying.sha512_update, ed25519.Signature.to_bytes, signature.error.Error, signature.error.Error.new]'
AUD = \$ ( mktemp '$HERE/.apex-XXXX.lean' )
PHASE 2 COMPLETE ON DALEK: THE FULL POINT-LEVEL LIFT
(verify_accepts_iff_decompress, button-enforced)
THE THEOREM: under the apex hypotheses, the signature's R bytes
DECOMPRESS to a valid on-curve point Pt, and
verifier accepts <=> Pt = [k]*(-A) + [s]*B (as points)
- accept iff decompress(R) equals the recomputed point. Every link of
the chain (byte comparison <-> canonical-encoding equality <-> point
equality <-> decompressed-point equality) is machine-checked over the
extracted code. Axiom cone EXACTLY the SHA-512 + wire-format boundary;
Phase 3b now enforces FOUR certificate tiers (byte apex, half-lift,
point equation, full lift).
Proofs/DecompressMain.lean:
- edwards_d_denote: the extracted EDWARDS_D constant denotes THE curve
d (edwards_d_spec + edD_char cancelled by 121666 nonzero).
- decompress_of_canonical (standard three axioms): canonical encodings
of valid on-curve points decompress to them - from_bytes recovers the
y-residue exactly (sign bit discarded), Q's own x witnesses the
square so sqrt_ratio_i returns the even root, the sign bit (Q's
x-parity, from byte 31) selects +/-root, and the parity-injectivity
argument pins the selection to edX Q; the assembled {X,Y,1,X*Y} is
ExtValid and on-curve.
- verify_accepts_iff_decompress: the capstone composition.
Full button green fresh. Remaining: replicate x3, coherence pass 4.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 22:05:55 +00:00
{ echo 'import Proofs.SigApexSpec' ; echo 'import Proofs.PointLiftSpec' ; echo 'import Proofs.PointEqSpec' ; echo 'import Proofs.DecompressMain' ; echo '#print axioms CurveFieldProofs.verify_accepts_iff' ; echo '#print axioms CurveFieldProofs.verify_accepts_iff_point' ; echo '#print axioms CurveFieldProofs.verify_accepts_iff_point_eq' ; echo '#print axioms CurveFieldProofs.verify_accepts_iff_decompress' ; } > \" \$ AUD\"
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
OUT = \$ ( LEAN_TIMEOUT = $TIMEOUT LEAN_MEM_MB = 4096 '$HERE/lean-guard' \" \$ AUD\" 2>& 1)
echo \" \$ OUT\"
2026-07-28 15:31:54 +00:00
rm -f \" \$ AUD\" \" \$ { AUD%.lean} .olean\"
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
FLAT = \$ ( echo \" \$ OUT\" | tr '\\n' ' ' | tr -s ' ' )
PHASE 2 HALF-LIFT PROVEN: verify_accepts_iff_point, button-enforced
THE THEOREM (CurveFieldProofs.verify_accepts_iff_point): for a parsing
signature, a valid on-curve public-key point, a canonical signature
scalar, and a successful recompute, there is a point R' - the certified
[k](-A) + [s]B, ExtValid and on-curve - with
verifier accepts <=> bytesVal R_bytes
= (edY R').val + ((edX R').val % 2) * 2^255
The apex's byte-for-byte comparison IS point-encoding equality: the
signature's R bytes are accepted exactly when they are THE canonical
encoding of the recomputed point. Axiom cone: EXACTLY the apex boundary
(SHA-512 oracle + wire-format opaques; zero curve/scalar/backend axioms),
now enforced for BOTH apex and half-lift by check.sh Phase 3b.
New machinery in Proofs/PointLiftSpec.lean:
- bind_ok_inv: generic ok-inversion of one monadic bind - the clean way
to invert oracle-bearing chains (axioms cannot be walked).
- recompute_inv: names the recompute chain's intermediates (hash, k,
-A, R') with their defining equations, via eight flat bind_ok_inv
steps after the pass-through reductions.
- Bytes64.exists_bytes + List.exists_len32: the 64-byte destructure -
Lean's match refuses list patterns beyond ~32 elements, so the device
is a 32-cons prefix + a list-level 32-destructure on the tail.
- The assembly: recompute_inv + from_bytes_mod_order_wide_spec (k
canonical) + edwards_neg_law (-A) + vartime_dsm_basepoint_spec (R',
valid, on-curve) + ed_compress_spec (er = canonical encoding) +
rangeEq_iff_bytesVal (byte comparison = value equality), threaded
through the ok-injectivity of the inverted equations.
Full button green fresh, incl. the extended Phase 3b.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 14:06:23 +00:00
if echo \" \$ FLAT\" | grep -qF \" 'CurveFieldProofs.verify_accepts_iff' depends on axioms: \$ ALLOWED\" \
2026-07-05 16:27:25 +00:00
&& echo \" \$ FLAT\" | grep -qF \" 'CurveFieldProofs.verify_accepts_iff_point' depends on axioms: \$ ALLOWED\" \
PHASE 2 COMPLETE ON DALEK: THE FULL POINT-LEVEL LIFT
(verify_accepts_iff_decompress, button-enforced)
THE THEOREM: under the apex hypotheses, the signature's R bytes
DECOMPRESS to a valid on-curve point Pt, and
verifier accepts <=> Pt = [k]*(-A) + [s]*B (as points)
- accept iff decompress(R) equals the recomputed point. Every link of
the chain (byte comparison <-> canonical-encoding equality <-> point
equality <-> decompressed-point equality) is machine-checked over the
extracted code. Axiom cone EXACTLY the SHA-512 + wire-format boundary;
Phase 3b now enforces FOUR certificate tiers (byte apex, half-lift,
point equation, full lift).
Proofs/DecompressMain.lean:
- edwards_d_denote: the extracted EDWARDS_D constant denotes THE curve
d (edwards_d_spec + edD_char cancelled by 121666 nonzero).
- decompress_of_canonical (standard three axioms): canonical encodings
of valid on-curve points decompress to them - from_bytes recovers the
y-residue exactly (sign bit discarded), Q's own x witnesses the
square so sqrt_ratio_i returns the even root, the sign bit (Q's
x-parity, from byte 31) selects +/-root, and the parity-injectivity
argument pins the selection to edX Q; the assembled {X,Y,1,X*Y} is
ExtValid and on-curve.
- verify_accepts_iff_decompress: the capstone composition.
Full button green fresh. Remaining: replicate x3, coherence pass 4.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 22:05:55 +00:00
&& echo \" \$ FLAT\" | grep -qF \" 'CurveFieldProofs.verify_accepts_iff_point_eq' depends on axioms: \$ ALLOWED\" \
&& echo \" \$ FLAT\" | grep -qF \" 'CurveFieldProofs.verify_accepts_iff_decompress' depends on axioms: \$ ALLOWED\" ; then
2026-07-06 02:01:15 +00:00
echo ' apex + full-lift axiom cones = exactly the SHA-512 + wire-format boundary (no curve/scalar/backend axioms)'
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
else
PHASE 2 HALF-LIFT PROVEN: verify_accepts_iff_point, button-enforced
THE THEOREM (CurveFieldProofs.verify_accepts_iff_point): for a parsing
signature, a valid on-curve public-key point, a canonical signature
scalar, and a successful recompute, there is a point R' - the certified
[k](-A) + [s]B, ExtValid and on-curve - with
verifier accepts <=> bytesVal R_bytes
= (edY R').val + ((edX R').val % 2) * 2^255
The apex's byte-for-byte comparison IS point-encoding equality: the
signature's R bytes are accepted exactly when they are THE canonical
encoding of the recomputed point. Axiom cone: EXACTLY the apex boundary
(SHA-512 oracle + wire-format opaques; zero curve/scalar/backend axioms),
now enforced for BOTH apex and half-lift by check.sh Phase 3b.
New machinery in Proofs/PointLiftSpec.lean:
- bind_ok_inv: generic ok-inversion of one monadic bind - the clean way
to invert oracle-bearing chains (axioms cannot be walked).
- recompute_inv: names the recompute chain's intermediates (hash, k,
-A, R') with their defining equations, via eight flat bind_ok_inv
steps after the pass-through reductions.
- Bytes64.exists_bytes + List.exists_len32: the 64-byte destructure -
Lean's match refuses list patterns beyond ~32 elements, so the device
is a 32-cons prefix + a list-level 32-destructure on the tail.
- The assembly: recompute_inv + from_bytes_mod_order_wide_spec (k
canonical) + edwards_neg_law (-A) + vartime_dsm_basepoint_spec (R',
valid, on-curve) + ed_compress_spec (er = canonical encoding) +
rangeEq_iff_bytesVal (byte comparison = value equality), threaded
through the ok-injectivity of the inverted equations.
Full button green fresh, incl. the extended Phase 3b.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-05 14:06:23 +00:00
echo 'APEX AUDIT FAILED: apex/half-lift cone is not the documented boundary' ; exit 1
THE SIGNATURE APEX: the EdDSA verification equation, proven and audited
`Proofs/SigApexSpec.lean`:
- `verify_loop_full` — the extracted 32-byte comparison loop returns exactly
the byte-equality of the two arrays (induction; axiom cone = exactly
[propext, Classical.choice, Quot.sound]).
- `verify_accepts_iff` — THE APEX: for a signature that parses, the
extracted RustCrypto verifier accepts IFF the recomputed compressed point
compress( [s]·B − [k]·A )
equals the signature's R byte-for-byte. The recomputation is grounded in
the PROVEN curve model (every curve and scalar call is a certified
definition); k is whatever scalar the SHA-512 oracle produces — the
honest EdDSA acceptance criterion with the hash opaque.
Boundary hygiene forced by the audit itself:
- The public vartime_double_scalar_mul_basepoint dispatch pulled the AVX2
vector-backend axiom into the apex cone. Fixed at the build level:
extract.sh pins RUSTFLAGS --cfg curve25519_dalek_backend="serial", so the
SIMD arm compiles out; BackendKind has only Serial and
get_selected_backend becomes a real definition (ok Serial).
- subtle.Choice.unwrap_u8 upgraded from axiom to the documented model
definition (Choice := U8; unwrap_u8 = self.0) — it sits on the verify
path via compress → is_negative.
- CurveSig modules added to GEN_MODULES (stale-olean incoherence otherwise).
check.sh grows Phase 3b: the apex certificate's axiom cone must equal
EXACTLY
[propext, Classical.choice, Quot.sound,
ed25519.Signature, sha2.Sha512,
sha512_new, sha512_update, sha512_finalize_bytes,
ed25519.Signature.to_bytes, signature.error.Error, Error.new]
— the SHA-512 hash oracle plus the opaque wire-format types. NO curve
axioms, NO scalar axioms, NO backend axioms, enforced on every button press.
Full check.sh green: 16 standard certificates + the apex audit.
Phase 2 (the point-level equation [s]B − [k]A = decompress R, needing
to_bytes canonicity and decompress) remains deferred and documented.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-04 17:45:55 +00:00
fi
"
2026-07-02 12:17:44 +00:00
echo ""
echo "ALL PROOFS PASS. ALL CERTIFICATES AXIOM-CLEAN. NO DEAD FILES."