dalek-ed25519-verified/verification/check-scalar.sh
saymrwulf ff1eea473d scalar layer: prove Scalar52::sub borrow + conditional-add-L carry chains
New in Proofs/ScalarSubSpec.lean (all axiom-clean [propext, Classical.choice,
Quot.sound], no sorry, no native_decide):
- nat_and_mask52 / nat_shift52 / nat_shift63 : 52/63-bit ops -> %,/
- sub_step_arith : isolated per-limb borrow accounting (tiny ℕ context,
  correction-on-the-left so no truncated subtraction) — the METHOD-4
  discipline that keeps 2^260-scale coefficients out of any one certificate
- sub_loop_spec : the FULL 5-limb borrow chain of Scalar52::sub, unrolled
  via loop_step/range_next_*; wrapping_sub, 52-bit mask store, borrow-out
  bit. This is the loop unroll that blocked the earlier attempt.
- csel_step : step-spec for the subtle conditional_select (faithful model)
- cond_add_l_zero_spec / cond_add_l_one_spec : BOTH cases of conditional
  add-of-L, full carry chains; the condition-1 case steps the addend as a
  clean value so the index_mut write-back matches sub_loop's pattern
- sub_telescope / add_telescope : the 2^52i-weighted value telescopes to
  2^260, discharged by omega (no kernel-capacity blowup)

check-scalar.sh: ScalarSubSpec added to the compile manifest; Phase-3 axiom
audit extended to sub_loop_spec + cond_add_l_one_spec (3/3 clean). Full
button green.

Honest boundary: top-level sub_val_spec (⟦sub a b⟧ = ⟦a⟧-⟦b⟧ in ZMod ℓ)
is documented as remaining — every lemma it needs is proven; what's left is
the Aeneas binding-arity for destructuring sub_loop_spec's pair-valued
multi-existential postcondition inside the do-block, a mechanical not a
mathematical gap. No sorry shipped (Invariants H1/H4).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-03 16:26:24 +02:00

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#!/usr/bin/env bash
# Scalar-layer check (Scalar52 arithmetic mod ). Compiles the gen model + the
# proven foundation. add/sub (Range-loop reductions) and the Montgomery mul
# path are in progress — see README. Guarded compiles throughout.
set -uo pipefail
source ~/aeneas-toolchain/env.sh
HERE="$(cd "$(dirname "$0")" && pwd)"
AENEAS_LEAN="$AENEAS_HOME/backends/lean"
GEN=(CurveScalar/TypesExternal CurveScalar/Types CurveScalar/FunsExternal CurveScalar/Funs)
PROOFS=(ScalarDenote ScalarLoop ScalarSubSpec)
echo "=== stub/axiom audit ==="
grep -rnE '^(private |protected |noncomputable )*axiom ' "$HERE"/Proofs/Scalar*.lean 2>/dev/null && { echo "axiom under Proofs/"; exit 1; }
echo " clean"
echo "=== compile (guarded) ==="
cd "$AENEAS_LEAN"
lake env bash -c "
set -uo pipefail
cd '$HERE/gen' && export LEAN_PATH=\"\$LEAN_PATH:\$PWD:$HERE\"
for m in ${GEN[*]}; do echo \" · gen \$m\"; LEAN_TIMEOUT=300 LEAN_MEM_MB=6144 '$HERE/lean-guard' \"\$m.lean\" || exit 1; done
cd '$HERE'
for m in ${PROOFS[*]}; do echo \" · proof \$m\"; LEAN_TIMEOUT=300 LEAN_MEM_MB=6144 '$HERE/lean-guard' \"Proofs/\$m.lean\" || exit 1; done
" || { echo FAIL; exit 1; }
echo "=== Phase 3: axiom audit (kernel-level) ==="
cd "$AENEAS_LEAN"
lake env bash -c "
set -uo pipefail
export LEAN_PATH=\"\$LEAN_PATH:$HERE/gen:$HERE\"
cd '$HERE'
AUD=\$(mktemp '$HERE/.audit-scalar-XXXX.lean')
{ echo 'import Proofs.ScalarDenote'; echo 'import Proofs.ScalarSubSpec'; echo '#print axioms ScalarProofs.L_val'
echo '#print axioms ScalarProofs.sub_loop_spec'
echo '#print axioms ScalarProofs.cond_add_l_one_spec'; } > \"\$AUD\"
OUT=\$(LEAN_TIMEOUT=120 LEAN_MEM_MB=4096 '$HERE/lean-guard' \"\$AUD\" 2>&1)
echo \"\$OUT\"
rm -f \"\$AUD\" \"\${AUD%.lean}.olean\"
N=\$(echo \"\$OUT\" | grep -cF \"depends on axioms: [propext, Classical.choice, Quot.sound]\" || true)
[ \"\$N\" -eq 3 ] || { echo \"AXIOM AUDIT FAILED: \$N/3 clean\"; exit 1; }
" || { echo FAIL; exit 1; }
echo " L_val axiom-clean"
echo ""
echo "SCALAR FOUNDATION: gen compiles; denotation + group-order constant (L = ) proven."