Tooling: 2.03× faster parity-side basis/contains with identical receipts

[VictorLiwentao]

Change and scope

At base 0b1cccf86e2f5132ed286a26ef0a681a495740ea, the historical parity-side audit spends most time in scripts/binary_phase_frames.py: basis and contains are called millions of times, and contains previously rebuilt basis(space) twice per membership test.

This PR memoizes basis on the row tuple and implements contains by reducing the vector against one basis of the space. The highest-bit pivot rule, elimination order, classify/nullspace/residual APIs and every Boolean result are unchanged. Only the source pin for scripts/binary_phase_frames.py changes inside the three certificates that bind that file (parity-side, disjoint-tensor-compression, dyadic-central-factor).

Tooling improvement; no new kappa. Selected frontier untouched.

Result

On Linux / CPython 3.12.3, five alternating fresh-process pairs of the full h=8,10,26 stream gave median 27.349 → 13.463 s (2.03×). Timing is host-descriptive and is not a correctness gate. Every experiment receipt matches the baseline checker fieldwise.

Package: research/parity-side-basis-cache/.

Validation

python3.12 -I -B research/parity-side-basis-cache/verify.py
python3.12 -I -O -B research/parity-side-basis-cache/verify.py
python3.12 -B scripts/research_package.py --package research/parity-side-basis-cache
python3.12 -I -B research/parity-side-basis-cache/benchmark.py --rounds 5

Expected:

PASS_PARITY_SIDE_BASIS_CACHE h=[8, 10, 26] roles=[724, 2271, 82720] repaired=[938, 3283, 308336] ... no_new_kappa
PASS_REGISTERED_RESEARCH_PACKAGE research/parity-side-basis-cache outcome=completed
PASS_IDENTICAL_PARITY_SIDE_RECEIPTS

Default verify is read-only. Full make verify, selected cold replay, Lean, and multiplication-theorem obligations were not rerun for this isolated historical-checker change.

Overlap and credit

Closest priors (different objects): CrocSwap/integer-mult-bounds#756, CrocSwap/integer-mult-bounds#1793, CrocSwap/integer-mult-bounds#1217. No competing open PR on this object at refresh.

Douglas R. Colkitt authored the parity-side obstruction, repair and original binary phase-frame checkers. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.

[Mister-Meeseeks]

Review found a cache-dependent validation regression in binary_phase_frames.basis at head 54d7f5fd4ef6073b6399d1e6e73773f61fe4360a:

_basis_cached.cache_clear()
basis((1,))       # warms the cache
basis((1.0,))     # now returns (1,), bypassing the integer assertion

The baseline rejects (1.0,), and your optimized implementation also rejects it with an empty cache. Validation inside the memoized function is skipped because these tuple keys compare equal. Please validate row types before lookup (or preserve element types in the key), add a warm-cache regression control, and refresh the affected source pins. Integer-input receipt equivalence remains useful; this hold concerns preserving verifier rejection behavior.