[petalas]

Summary

The complete pinned PR1668 replay spends time multiplying binary incidence zeros by kernel coefficients. A source-bound adapter replaces only that predicate:

- sum(row[j] * vector[j] for every coordinate j)
+ sum(vector[j] for j in the row support)

Claim type: scoped implementation-equivalence proof, exact operation-count certificate and local performance evidence. The complete workload removes 15,732,800 zero products and 1,408,228 unit multiplications. Its scientific stdout and every reached kernel result are identical. Fifteen alternating fresh-process pairs reduce median direct replay time from 1.801392 s to 1.604257 s, 10.94%; every pair improves and all thirty outputs agree. Ranges are 1.787448–1.983607 s and 1.573416–1.769150 s. This is local to CPython 3.12.15 on a shared macOS arm64 host, not a portable speed guarantee.

The original scientific source and credit stay unchanged. Its SHA256 is authenticated before compilation, and optimize=0 retains its assertions under an optimized adapter. No rank, geometry, fixture, scientific control or theorem changes. Discovery stopped at this first verified improvement.

This contribution was produced by Nick Petalas. Credit Josie Elliston / PR1668 and PR1650, Andrey Mas / PR1560, Aaron Wang / PR1649 and the retained Brett Halligan, themilkman216 and DreamingOfClouds decoder lineage. Sparse dot products are classical; the new contribution is the bounded adapter and its exact complete-workload saving. The predecessor mathematical result is cited, not independently audited or claimed as new.

Evidence

• Before: 17,141,028 coordinate products in the complete workload. After: 1,408,228 selected-coordinate sum terms and no scalar multiplications inside those dots. Both source authentication and validation overhead are paid by the complete timed process.
• The conformance verifier compares all 148 reached calls and 353,069 short-circuit-ordered dots, complete scientific stdout, 55,987 small binary/ternary dot fixtures and fourteen controls. The complete scientific stdout SHA256 is 5ece3cdbfec55235c3d95cfcf7bae6448b31cc6b7d4504676c06a7200ec9ce4b.
• Both warning-strict normal and optimized registered commands pass locally, measured at 4.44 s and 4.46 s in direct runs, below their 120 s limits. Metadata/pins and the committed-byte/source-history preflight pass on eight package/input files. The complete registered replay passes on the publication commit.
• Official export integrity and declared-input coverage pass. A read-only Git-free optimized replay with empty PATH/PYTHONPATH passes with every exported file unchanged.
• Separate profiles attribute about 24.4% of baseline instrumented main time to the changed kernel products. Fraction elimination remains the dominant unchanged cost. Timing includes the whole direct replay; it excludes the extra conformance runner and CI environment setup. The README retains all fifteen raw timing pairs and the discarded preliminary measurement conditions.

Reproduce from the repository root with the exact available interpreter, or substitute another absolute CPython 3.12 path:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/frame-kernel-sparse-products/replay.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/frame-kernel-sparse-products/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/frame-kernel-sparse-products/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/frame-kernel-sparse-products
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/frame-kernel-sparse-products --check-source-history
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/frame-kernel-sparse-products/benchmark.py --pairs 15

Expected conformance marker: PASS_FRAME_KERNEL_SPARSE_PRODUCTS. Receipts are generated on stdout and bind package bytes; no receipt is handwritten. Sparse checkouts must materialize this package and research/full-family-g-without-d.

Limitations

This accelerates one exact scientific replay. It supplies no independent mathematical acceptance, new kappa, native supplier, physical caller, recursive invoice or selected-frontier change. All five selected framework assumptions remain. No P105 runtime is inferred. Timing is observational and is not a CI gate. Independent human and formal proof-kernel review, Lean, Docker and the complete selected scientific cold replay are unrun. No required local mathematical or implementation check is deferred to CI.

The executable has bounded row/vector shapes. Python allocation, the fixed-hash reference loader, the bounded comparison callback and the retained source's depth-eight frame enumeration have explicit implementation-scope deviations in the README. No general arbitrary-object or streaming-iterator replacement contract is claimed.

Open next questions

Can a separately budgeted larger incidence replay benefit from the same binary-row contraction? First profile one complete command and prove every replaced row is binary. A source-bound larger workload, its complete conformance evidence and its end-to-end performance remain missing. No rank or geometry optimization is included here.

Related open work

• PR2375 accelerates production frame-pair enumeration. This adapter changes kernel dot products in the separate complete PR1668 incidence replay, so its timings are different workloads and are not competing numerical estimates.
• PR6569 specializes exact dot products in the complete PR3166 E8 root-swap replay. This package contracts binary incidence rows in the separate PR1668 command; the runtimes measure different complete workloads and do not give competing estimates for one command.

The completion refresh listed the thirteen other account open PRs created since the advance CLAIM and screened their titles and bodies for this exact source and quantity. PR6569 is the adjacent replay-engineering contribution listed above; PR6565 studies different Schur/header counts. No competing computation of this exact command or disagreement in a shared computed number was identified. No extra computations audited another contribution.

The live exact-source search found no open PR changing the PR1668 kernel predicate. Main and merged-object searches, current claims and this account's recent work were checked before committing. The broader helper covered 506 open PRs and 6,503 Discussion records; sparse local notes, arbitrary historical diffs and unpublished work remain coverage limits. Advance CLAIM.

CI notes

Both hosted checks passed at exact head a5f300a6358543eaa4bb6fe75b8054398cac273b in run 41610572423: plan in 4m30s and registered package replay in 1m41s. The completed checks were read once. Separate run metadata confirms the matching head, completed status and successful conclusion.

Both registered normal/optimized commands and the local metadata, byte/ancestry and export checks passed. CI certifies execution of the registered implementation-conformance checks. The local timing percentage and the predecessor mathematical theorem are not independently certified by CI. No check failed; independent human and formal proof-kernel review remain unclaimed.

Merge Danger

Door: two-way. Blast radius: one isolated opt-in research package. The retained source, shared replay machinery and selected result are unchanged.