[petalas]

Summary

Reduce complete rational parameter solve-and-check wall time by 15.49% on a declared six-parameter workload, preserving every certificate byte. Median time is 0.079004 → 0.066770 seconds across seven alternating runs per arm, with disjoint ranges and zero errors.

 complete rational-box CLI, unchanged basis order and primal-dual checker
-  Fraction Gauss-Jordan square solves
+  row-wise denominator clearing
+  fraction-free integer elimination and exact back substitution

Claim type: scoped implementation proof, finite correctness evidence and a local performance measurement. This is a new opt-in implementation of the complete parameter caller, not an audit of its predecessor. No new kappa or LP theorem is claimed. Only research/rational-box-fraction-free/ is added.

The contribution was produced by Nick Petalas. Credit Ali Romman / PR5792 for the original bounded optimizer, exact dual checker, regression tests and guide; zxv for the inherited parser helpers; and classical fraction-free elimination, Sylvester identities and LP duality. All predecessor bytes and credits remain unchanged.

Evidence

• Before: a separate complete-optimizer profile places 0.099 of 0.123 profiled seconds in 814 square solves. Profiled times are excluded from the benchmark.
• After: seven alternating complete CLI solve/check pairs per arm, each including two fresh interpreters, actual optimization, certificate serialization and a separate certificate check. Every output reports objective 24 and 757 examined bases and is byte-identical. Baseline wall range 0.077945..0.080634 seconds; candidate 0.066205..0.069032. Median child CPU time is 0.075766 → 0.063610 seconds. No cached optimum is used.
• Local warning-strict normal and optimized checks pass: 5,985 exact systems, including 1,161 independently classified singular cases in the exhaustive two-dimensional domain; eight kernel controls; six inherited regression groups; complete exported CLI byte equality; all three actual source corruptions reject before engine import. The written argument covers the bounded interface; the census corroborates it.
• Registered package replay passes in both modes. Direct registered checks were timed locally at about 0.46 and 0.50 seconds, below their 120-second limits; the final combined registered run took 1.30 seconds.
• Committed bytes and source ancestry pass for all 12 package/input files at d2d0d6cd0d1445e534e68983d1b06e201432e556. Official export integrity passes. Both complete read-only, Git-free exported replays pass and produce identical receipts. In-memory compilation and whitespace checks pass.

Exact reproduction from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B -W error research/rational-box-fraction-free/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -O -B -W error research/rational-box-fraction-free/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/rational-box-fraction-free
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/rational-box-fraction-free --check-source-history
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B -W error research/rational-box-fraction-free/benchmark.py

Any CPython 3.12 interpreter may replace that local path. Standard library only. The verifier and benchmark print generated source-hash-bound receipts. IMB_RUN_DIR can select an existing external scratch directory. The benchmark records every raw sample and checks source stability before and after measurement. It is deliberately outside the CI gate.

Measurement environment: macOS 27.0.1 arm64, CPython 3.12.15, 18 logical CPUs, unreserved host with another Python process active. The README contains every raw wall-time sample, the exact workload, proof, limits and overlap coverage. This is one bounded parameter-tool workload, not a supplier invoice or a uniform performance guarantee. The predicted implementation scope in the advance CLAIM is delivered, and work stopped at the first passing improvement.

Limitations

The original limits remain six parameters, 24 total rows, at most 50,000 active bases, a checked feasible incumbent and rational input magnitudes through 10^9. The runner is opt-in and authenticates exact source bytes. The optional benchmark uses POSIX resource; Windows performance is unclaimed. External Python linters were unavailable.

No source-to-constraint proof, native supplier, physical ownership/restoration, precision/tape implementation, compiler admission, selected scientific replay, Lean or Docker run is supplied. The selected frontier and all five framework assumptions remain unchanged. Independent human and formal proof-kernel review are unclaimed.

Open next questions

1. Can the unchanged complete feasibility checks be accelerated without changing the first optimal basis or output bytes? Begin with a separate profile after this kernel and retain a new complete-path comparison.
2. Which authenticated supplier parameter problem benefits from this complete solver? Derive every row from one pinned full bill and certify a positive margin; an LP optimum alone does not establish physical legality.

Related open work

• PR6272 uses denominator clearing for complete rational-rank certificate product checks. It changes a different source script and caller; this PR changes square elimination in the bounded rational-box optimizer. No timing or certificate-count comparison is asserted.

The completion refresh inspected all thirteen open account PRs created since the advance CLAIM, including this PR. None of the twelve other contributions targets this rational-box optimizer or its complete solve/check workload. No same-instance numerical disagreement was identified, and no extra computations checked other submissions. PR5792 is merged and remains the credited source. Search coverage is bounded and does not prove global novelty.

CI notes

Both hosted checks, plan and replay (research/rational-box-fraction-free), passed at exact head d2d0d6cd0d1445e534e68983d1b06e201432e556 in run 41066931363. The completed checks were read once; separate run metadata confirms completed status, success and the matching head. All declared local checks and publication/export controls above also pass. Hosted replay certifies the registered finite checks and source bindings. The local timing measurement remains outside the CI gate; independent human and formal proof-kernel review are unclaimed.

Merge Danger

Door: two-way. The isolated opt-in package can be removed without changing default commands or predecessor sources.

Blast Radius: isolated. This adds no shared-code, selected-frontier or dependency changes.