[petalas]

Summary

The complete PR1294 scientific caller spends time multiplying zero left entries. An isolated integer row-expansion adapter removes exactly 255,310 scalar products and reduces local median complete-caller time by 17.87%, with identical complete scientific output.

 matrix multiplication
- enumerate every left/right scalar product
+ expand each nonzero left entry against its right row
 complete symbolic and dense scientific consumers
   unchanged

Claim type: scoped implementation-preservation proof, exact finite conformance and local performance evidence. No new mathematical identity, kappa or selected-frontier change. This contribution was produced by Nick Petalas.

Credit Philipp / mightyOil PR1294 for both complete consumers, their identities, receipts, tests and original implementation; Charles Bethin PR1278, Hanson Sun PR1244/1085, Chafik Boukhalfa PR628/905, Gareth Davidson PR877 and their retained lineage. Distributivity and sparse multiplication are classical. The predecessor mathematics is preserved input, not an audit deliverable. Advance CLAIM.

Evidence

• Before: 562,574 scalar products. After: 307,264. All 16,294 reached calls match the original and preserve inputs. Both complete scientific receipts and all six retained package tests remain.
• All 6,626 additional integer/rectangular cases, sixteen source rejection controls and eight arithmetic rejection controls pass. Four faulty kernels are rejected by the actual complete consumer.
• Five alternating fresh-process pairs have zero failures and byte-identical stdout. Original median/range: 0.074929500 / 0.074595417–0.075584708 seconds. Candidate median/range: 0.061536584 / 0.060592416–0.062196792 seconds. Every pair improves; ranges are separated. README retains every pair, the limiter profile and environment. This local measurement is not a CI performance threshold.
• The timed boundary includes process startup, fourteen-input authentication, module loading, both complete scientific bodies, receipt comparison and full output. Retained package tests, new conformance, metadata and CI planning run separately. No reduction of the whole generic CI job is claimed.
• Warning-strict normal and optimized registered checks pass locally in 0.7013 and 0.7668 seconds. Metadata, source pins, compilation and whitespace checks pass. All 21 committed package/input files and declared source ancestry pass. Official export integrity and a Git-free optimized replay with an empty PATH pass with the identical generated verification receipt.

Reproduce from the contribution checkout root with CPython 3.12 and its standard library:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/dirty-phase-row-products/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/dirty-phase-row-products/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/dirty-phase-row-products
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/dirty-phase-row-products --check-source-history
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/dirty-phase-row-products/benchmark.py

Another CPython 3.12 interpreter may replace the local path. Expected markers are PASS_DIRTY_PHASE_ROW_PRODUCTS, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. Receipts and benchmark reports are generated, with source/program hashes. Set TMPDIR to a private external directory for local temporary fault fixtures.

Limitations and unrun obligations

The adapter supports the exact rectangular integer matrix contract; custom scalars, floating point and malformed matrices are outside scope. It is opt-in and does not modify the predecessor commands. Physical callers, rounded leaves, native/stock/precision/tape/compiler admission and the complete multiplication theorem remain separate. No selected cold replay, native suite, Lean or Docker run was needed. All registered commands ran locally. Independent human and formal proof-kernel review are unclaimed.

Canonical main was fetched again before committing and remained 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8, selected PR6030. Live open PRs, claims, main and merged general/object/formula searches were refreshed. Sparse historical notes and unpublished work remain coverage limits.

Open next questions

Should a maintained replay adopt the kernel? First profile one named consumer, confirm its integer matrix contract and compare the complete command with caller-specific conformance. Default adoption and a selected-caller gain are not supplied here.

Related open work

No other PR in the refreshed live searches studies this complete PR1294 multiplication consumer.

• Speed up the complete current P104 native replay by 2.74x #6479 optimizes the current P104 Clifford native replay; its circuit evaluator and scientific consumer differ. No common timing or arithmetic count is compared.

• Reduce orthogonal-witness guard from 228 to 182 bits (no κ) #6481 improves an orthogonal-witness rounding guard; its numerical detector differs from this exact dirty-phase replay. Its guard and the runtime measured here are different quantities.

• Reduce complete D8 replay time by 27.09% (no κ) #6492 optimizes the complete PR1443 D8 replay through packed transition arithmetic. Its source, transition workload and timing fixture differ from this PR1294 matrix consumer; no common runtime or scalar-product count is computed.

The completion refresh inspected fourteen account open PRs created since the advance CLAIM, including this PR. None of the thirteen others studies this exact complete consumer or computes a conflicting value for its reached products. No extra scientific computations audited another contribution.

CI notes

Both hosted checks passed at exact contribution head a0997c920567e78b2484da49ba2d77f853cca1ca in Registered research packages run 41555485920: plan in 4m29s and registered package replay in 1m22s. The completed checks were read once; run metadata confirms this head, completed status and successful conclusion. The replay executes both registered warning-strict normal and optimized checks.

All registered commands, metadata, committed-byte/source-history and Git-free export checks also passed locally. No required check was left solely to CI. Hosted replay certifies execution of the bounded registered checks; the 17.87% timing result remains local evidence and is not remeasured by CI. Independent human and formal proof-kernel acceptance remain unclaimed.

Merge Danger

Door: two-way. Blast radius: isolated. Seven new files under one package; shared code, predecessor files, frozen evidence and selected-frontier records are unchanged.