Canonicity pass (the layer is now closed under its own preconditions):
- sub_val_spec post carries the exact value equation
(exists beta <= 1, scVal r + scVal b = scVal a + ell*beta, with the
underflow guard beta = 1 -> scVal a < scVal b)
- add/montgomery_reduce/mul/aggregate posts all carry scVal r < ell:
canonical inputs give canonical outputs everywhere. Needed because
from_bytes_wide (hash-to-scalar) feeds Montgomery outputs into add.
Hash-to-scalar foundation (toward Scalar::from_hash / EdDSA verify):
- extraction scope + from_bytes_wide (brings constants::R); regenerated gen
- source repos carry a documented Aeneas-compat patch: the bare
`hi[4] = words[7] >> 20` extracts ill-typed at pin bf13c42e; masked
(semantic no-op, words[7] >> 20 < 2^44)
- Proofs/ScalarWideSpec.lean: R constant lemmas (R = 2^260 mod ell,
witness 2^260 = R + 255*ell) and montgomery_mul_spec, the single
Montgomery round: [r]*2^260 = [a]*[b], canonical bounded output
check-scalar.sh: 10 proof files, 11 kernel audits, all exactly
[propext, Classical.choice, Quot.sound]. Button pressed fresh: green.
Phase B - montgomery_reduce (Proofs/ScalarMontSpec.lean + Proofs/ScalarReduceSpec.lean):
- mont_key: LFACTOR*L0 + 1 = 214835089243030*2^52 (the -1 inverse identity, norm_num)
- mont_cancel: (s + ((s*LFACTOR) % 2^52)*L0) % 2^52 = 0 via Nat.ModEq - every
part1 shift is an EXACT division, nothing discarded
- part1_spec / part2_spec: per-round helpers (carry*2^52 = sum + p*L0; exact split)
- mont_head_telescope (E0-E4) and mont_tail_telescope (E5-E8): linear_combination
certificates with weights 2^52k; mont_bound: X' < 2*ell from Z < 2^260*ell
- montgomery_reduce_spec: post `scDenote r * 2^260 = Z` in ZMod ell + 52-bit bounds.
METHOD-4 split at the round-4/5 boundary: the 74-step monolith is
elaboration-pathological; each half compiles in ~25s/3GB.
- The single death-spiral line: an omega for the nonce-sum bound with ~110
hypotheses in context never returns; extracted to nonce_sum_bound (5 hypotheses,
instant). Bisected with fail-probes; documented in control-repo FAILURES.md.
Phase C - mul (Proofs/ScalarFullMulSpec.lean):
- RR_limbs/RR_scVal/RR_lt; RR_denote: RR = 2^520 - K*ell kernel-checked, so
⟦RR⟧ = R^2; R_isUnit: 2^260 unit of ZMod ell (coprime oddness witness)
- mul_spec: mul_internal -> montgomery_reduce -> mul_internal(*, RR) ->
montgomery_reduce composed; column values folded by `ring`; R cancelled via
IsUnit.mul_right_cancel. Hypothesis scVal a * scVal b < 2^260*ell (honest
Montgomery bound; canonical inputs satisfy it).
Aggregate (Proofs/ScalarMain.lean): scalar_add/sub/mul_correct on ScBnd
interfaces + canonical_mul_bound + scalarImplementation bundling all three.
sub_val_spec/add_val_spec posts strengthened with result-limb 52-bit bounds
(the montgomery tail feeds sub's output back into mul_internal).
check-scalar.sh: 9 proof files, 10 kernel audits (was 6), all exactly
[propext, Classical.choice, Quot.sound]. Button pressed fresh: green.
