[petalas]

Summary

The complete PR5210 finite nonlinear support caller takes 24.54% less local median wall time, with byte-identical complete RESULT/MATRICES and wrapper reports. Claim type: empirical implementation improvement with a scoped exact-arithmetic equivalence proof and finite conformance evidence. This contribution was produced by Nick Petalas. No new kappa or selected-frontier change.

authenticate the original evidence and all 46 source-package pins
run the unchanged complete finite main
replace each Fraction matrix product by Gaussian-integer numerators
restore one exact power-of-two denominator at the product boundary
compare complete generated files against both frozen modes

Only research/nonlinear-support-integer-products is added. Chris R / Clear1nsight retains PR5210's finite checker, controls, portable evidence wrapper and written theorem, together with the retained coded-native and released-operator lineage. Common-denominator arithmetic and sparse multiplication are classical. The bounded adapter and complete-caller integration are the new implementation contribution; no predecessor scientific audit is claimed.

Evidence

Eighteen fresh processes per mode use all six execution orders three times, on CPython 3.12.15/macOS arm64 with 18 logical CPUs and uncontrolled shared-host load. Zero failures; all complete reports agree. The integer caller wins all eighteen matched rounds against the original. All raw timings and the slow outlier are retained in the package README.

Complete caller	Median ms	Range ms
Original wrapper	98.860	97.538–131.133
Reference adapter with original product	86.495	85.847–89.032
Integer adapter	74.598	73.881–94.632

The overall improvement includes running the same finite main inside the authenticated runner instead of starting another child interpreter. The reference-adapter control isolates a further 13.75% median decrease from integer products, with seventeen of eighteen matched wins. The headline is not attributed to arithmetic alone. Startup, authentication, input copying, every check, complete output comparison and scratch cleanup are timed. No result cache is used. An untimed profile identifies Fraction products and zero comparisons as the changed work.

Local checks pass:

• All 277 actual matrix products and 70,912 entries agree with the retained engine; all complete RESULT/MATRICES files agree with both frozen modes; the unchanged original wrapper report agrees.
• 146 additional product fixtures, ten invalid-input cases, actual changed-source invalidation and an incorrect complex-sign mutation. Checks remain enabled under optimized Python.
• Both registered warning-strict normal/optimized commands complete locally in under one second each. No local package obligation is deferred to CI.
• Committed bytes, modes and declared source ancestry pass at head 9162454 for all 54 package/input files.
• Official export integrity and both direct modes pass from a read-only, Git-free export with an empty PATH. All 55 exported files, including the export manifest, retain their bytes.

The timing sample binds 662e18c. The later commit fixes write permission on the mutation tests' own temporary copies when the source export is read-only. Timed runner and arithmetic bytes are unchanged.

From the repository root, using the local interpreter or another CPython 3.12:

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

Expected markers: PASS_NONLINEAR_SUPPORT_INTEGER_PRODUCTS, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. The verifier emits a generated package-hash-bound receipt. The README gives the opt-in fresh-process benchmark command; its generated report binds the measured Python files. No receipt is handwritten.

Limitations

The adapter accepts square matrices through dimension sixteen, dyadic denominator exponents through sixty-four and Fraction numerators through 256 bits. Larger values and odd denominators are explicitly rejected. The complete fixed caller fits those bounds; arbitrary repeated products need not. A short written proof establishes exact product substitution and induction through this caller, with no all-width theorem extension.

This small calibration saves milliseconds. Local timing is not a portable speed guarantee. No physical/native supplier, 17-axis replay, compiler closure, precision/stock bill, selected scientific replay, Lean, Docker or complete multiplication theorem is supplied. Independent human and formal proof-kernel review are unclaimed. The selected kappa and its five framework assumptions remain unchanged.

Open next questions

Can a larger literal native/caller checker use this representation with a useful complete runtime gain? First profile its complete path and specify its denominator, dimension and coefficient bounds. A compatible caller contract and complete measurement remain missing. Optimization of this fixture stops at this first verified improvement.

Related open work

• Reduce complete rational-rank certificate time by 54.94% (no κ) #6272 accelerates rational-rank certificate product predicates using classical denominator clearing. This package integrates exact Gaussian-dyadic products into PR5210's fixed complete support caller, with its own source pins, controls and measurement.
• Reduce complete mapped-contact replay time by 72.54% (no new κ) #6274 accelerates PR4841's mapped-contact distance caller using binary basis ranks; its source geometry and complete caller differ from this Gaussian product calibration.
• Reduce complete pivot-440 forward replay time by 15.91% (no κ) #6276 prepares rational gate coefficients once in PR1431's pivot-440 forward replay; it changes a separate propagation caller.
• Reduce complete dirty-certificate replay time by 22.57% (no new κ) #6279 accelerates PR5235's dirty-circuit certificate traversal through a prefix cache; it changes a separate certificate caller.
• Reduce complete E7 replay time by 21.55% (no new κ) #6282 uses intersection counters in PR5729's complete E7 classification replay; its binary codeword engine is separate from this weighted-monomial caller.
• Reduce complete sparse recurrence CLI time by 45.68% (no κ) #6283 skips exact-zero elimination updates in PR5785's sparse coupled-recurrence CLI; it changes a separate rational certificate producer.

The account's open PRs created since the advance CLAIM were refreshed before DONE. No additional open PR studying the literal PR5210 checker or this product substitution was found. The adjacent replay improvements above have different fixtures and quantities; no mathematical agreement or disagreement, or numerical performance comparison, is asserted. This bounded search cannot exclude unpublished overlap. The cached helper had no usable remote snapshot; live PR/Discussion queries and direct main searches supplemented its incomplete local coverage.

CI notes

Both hosted checks, plan and replay (research/nonlinear-support-integer-products), passed at commit 91624547671bf2ed94e93818de86b8ac68cd36ea in run 41068858697. The completed checks were read once; run metadata separately confirms the matching head, completed status and successful conclusion.

Every registered command also passed locally, together with committed-byte/source-history/mode checks, export integrity and both read-only Git-free direct modes. Hosted conformance does not certify the local speed measurement or extend the predecessor's mathematical theorem. No local package obligation is left unrun.

Advance claim: #1166 (comment)

Merge Danger

Door: two-way. Blast radius: isolated. Removing this opt-in package restores the prior workflow; source evidence, shared code and selected-frontier files are unchanged.