Tooling: batch exact rows for the quadratic-affine rank witness (8.4x faster check, no new kappa)

[navinor]

Tooling improvement; no new kappa. Verification engineering (track 85-94, seed 89). Base commit 2921874911956718fcaaaf9396fe8267b3cfa9f0. Prepared with help from opencode.

What changes

scripts/audit_quadratic_affine.py (part of make verify-certificates) builds twelve exact quadratic-affine rank witnesses; its hot path rank_witness in scripts/experiments/quadratic_affine.py constructed each row with one inner call per (row, column) pair (160,135,378 calls in the heavy fixture). This replaces that loop with an exact bit-sliced batched engine (lane-packed character masks, even-lane SWAR zero test, collision-free staged stride-8 gather). inner, the fixtures and all mathematical outputs are unchanged.

Measured on the same host and input (CPython 3.13.15, Windows):

Run	Wall time
scripts/audit_quadratic_affine.py at base	89.1 s
scripts/audit_quadratic_affine.py with this change	10.6 s (8.4x)
Row construction, all fixtures, reference vs batched	67.0 s -> 3.56 s

The regenerated certificates/quadratic-affine-vectors.json differs from the base commit in exactly one line: the recorded hash of the edited source file. Every case record, row digest, binary rank and span control is byte-identical.

Verification

sh python3 -B research/quadratic-affine-performance/benchmark.py --out /tmp/qa-benchmark.json

Expected final line: PASS identical rows (14662 rows, 0 mismatches); certificate equals committed; controls: odd-lane false positive demonstrated, dropped gather stage detected.

All 14,662 witness rows (including all 12,623 rows of the heavy fixture) are compared against the verbatim base-commit reference engine; the full certificate is recomputed and required to equal the committed file, and the committed base-commit snapshot evidence/base-certificate.json must differ only in the edited source's hash. research/quadratic-affine-performance/test_engine.py (11 tests) adds brute-force primitive comparisons with borrow-chain adversaries, randomized family samples, unchanged rejection paths, and negative controls (odd-lane SWAR false positive; dropped gather stage; one-bit row corruption changing the digest). The suite was red-green verified: a deliberately dropped gather stage fails 5 tests. tests/test_quadratic_affine.py passes unchanged and python3 -B scripts/verify_selected_result.py still reports the selected kappa.

Overlap

PR 752 (Curtis Dransfield, seed 92) reached this hotspot first with a non-invasive packed-lane adapter (73.4 s -> 10.96 s on macOS arm64). Credit to them. This PR is an independent second implementation that additionally (1) wires the speedup into the shipped check so the default make verify-certificates run gets faster, (2) machine-checks the one-line certificate diff against a committed base-commit snapshot, and (3) corroborates the packed-lane conclusion from a different lane design with red-green verified negative controls.

Scope

No certificate content, bound, kappa value, patch, generator, proof supplement, pinned source or upstream/ file changes; only scripts/experiments/quadratic_affine.py, its regenerated certificate (one line), and the evidence package research/quadratic-affine-performance/. This is a finite-check speedup, not a formal proof of any theorem. The unchanged GF(2) elimination is now the runtime floor. Full make verify, the selected cold replay, Lean and remote Linux CI were not run; only the affected checks above were. Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at cced22b95fb5b485da05b8187c8a9754b6a8c85a.

This remains open after scoped triage. Next review step: Engine regressions pass and fixtures 0–10 compare exactly, but the full benchmark reached 180 seconds during the heavy fixture. Complete all 14,662 row comparisons and the fresh certificate/hash-only comparison before changing the default checker.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.

[navinor]

Continuation run for the outstanding whole-head obligations, at head cced22b95fb5b485da05b8187c8a9754b6a8c85a, per the continuation point in #1076 (comment) and the batch review doc https://github.com/CrocSwap/integer-mult-bounds/blob/main/docs/research/community-efficient200-review.md. Both outstanding checks are complete. No code was changed.

Environment: Windows 11, CPython 3.13.15. The python3 alias on this host is the broken Microsoft Store stub, so commands were run as python -B ... with the same interpreter the README's python3 -B refers to. All runs were blocking foreground runs under a 60-minute budget; the 180-second figure in the batch review is a triage budget, not a proof criterion.

1. Full differential benchmark — all 14,662 row comparisons

python -B research/quadratic-affine-performance/benchmark.py --out %TEMP%\qa-1076-scratch\benchmark.json

Total wall time 103.3 s. Per-fixture row comparisons of the shipped batched engine against the verbatim base-commit reference (inner per pair), with per-fixture wall times:

fixture	rows equal	reference	batched
0	3/3	0.000 s	0.000 s
1	3/3	0.000 s	0.000 s
2	5/5	0.000 s	0.000 s
3	23/23	0.001 s	0.000 s
4	23/23	0.001 s	0.000 s
5	45/45	0.002 s	0.000 s
6	383/383	0.054 s	0.006 s
7	383/383	0.055 s	0.007 s
8	765/765	0.200 s	0.018 s
9	23/23	0.000 s	0.000 s
10	383/383	0.049 s	0.005 s
11 (heavy)	12623/12623	68.358 s	3.454 s

Totals: 14,662 rows compared, 0 mismatches, including every one of the 12,623 rows of the heavy fixture that the earlier run reached its 180-second cap on. Row-construction totals across all fixtures: reference 68.719 s vs batched 3.491 s. The heavy fixture's full rank_witness (batched rows plus the unchanged GF(2) elimination) took 17.77 s on this host, rank 12623. Final lines of the run:

heavy rank_witness (batched engine): 17.77s, rank 12623
certificate equals committed; base-commit certificate differs only in: scripts/experiments/quadratic_affine.py
PASS identical rows (14662 rows, 0 mismatches); certificate equals committed; controls: odd-lane false positive demonstrated, dropped gather stage detected

Both negative controls behaved as required: the odd-lane SWAR false positive was demonstrated on a borrow chain, and a dropped gather stage was caught by the same row comparison. Timings above are measurements on this host, not acceptance thresholds; they differ from the host recorded in research/quadratic-affine-performance/README.md.

2. Fresh certificate recomputation and hash-only comparison

The certificate was recomputed through the package's own flow (audit_quadratic_affine.certificate() serialized with prepare_layers.serializable) and compared with the committed certificates/quadratic-affine-vectors.json:

• The recomputed certificate equals the committed certificate byte for byte.
• The committed base-commit snapshot research/quadratic-affine-performance/evidence/base-certificate.json differs from the recomputed certificate in exactly one line — the recorded hash of the edited source file scripts/experiments/quadratic_affine.py:

-    "scripts/experiments/quadratic_affine.py": "8f9252bd092eb14779997c6767e090377e91f4d57e6526e9840ae0dd7dcc8f9c",
+    "scripts/experiments/quadratic_affine.py": "124e33558b232aa7c684c332f2902dc437c0959fd13ce4b711f5ef923ed75a6f",

No other certificate field differs. The same one-line diff is what git diff 2921874911956718fcaaaf9396fe8267b3cfa9f0 HEAD -- certificates/quadratic-affine-vectors.json shows at the head under review.

3. Regression re-runs

python -B research/quadratic-affine-performance/test_engine.py

11 tests pass in 1.28 s (wall 1.7 s): Ran 11 tests ... OK.

python -B scripts/audit_quadratic_affine.py

Wall 13.2 s, output: PASS: twelve exact quadratic-affine core rejections, including Gaussian rank-two labels.

Obligations from the batch review doc

Now satisfied for #1076:

• All 14,662 row comparisons completed with 0 mismatches, including the full heavy fixture; the earlier 180-second triage run left this outstanding and implied no conclusion.
• The fresh certificate equals the committed certificate, and the committed base-commit snapshot differs from it only in the recorded hash line of scripts/experiments/quadratic_affine.py — the "one-line hash-only diff" claim is now machine-checked end to end.
• The direct reference comparison and failure controls that the batch review doc requires before considering a default-checker change are recorded above.

Still open, and not claimed here:

• Changing the default checker remains gated on maintainer acceptance; this run produces evidence for that decision and does not make it.
• No formal proof or theorem claim: this is finite evidence for a finite check. Per the batch review doc, no formalization is accepted from a Python source check alone. No kappa value, bound, certificate content, or mathematical claim changes.
• Timing ratios are measurements on one host, not independently claimed speedup thresholds.

Attribution: Aaron Wang / navinor, with help from opencode.