[petalas]

Summary

The complete PR5615 dyadic-capacity replay takes 9.83% less median wall time on the measured host. This is a scoped implementation-preservation proof and local performance result, with no new kappa.

exact determinant
  size 1 or 2: evaluate the one or two terms directly
  size 0 or 3..5: evaluate every term with a fixed signed permutation schedule
complete original capacity caller and every certificate predicate remain

The opt-in adapter changes only the exact determinant evaluator. It caches no matrix values, determinants, certificate decisions or scientific outputs. The original algorithm and sources retain their bytes. Credit Ali Romman / PR5615 for the algorithm, independent minor oracle, full caller and fixtures, PR5602/5599 and their retained helper/native/compiler lineage, including PR5609/5611 and Nick Petalas's earlier PR5115 row preparation. The new adapter, preservation proof and measurement were produced by Nick Petalas. Leibniz expansion and permutation parity are classical.

Evidence

Five alternating fresh-process pairs on macOS arm64, CPython 3.12.15, have zero failures and identical complete scientific outputs. Original median 0.131713167 s, range 0.130969667 to 0.142122583 s; scheduled median 0.118766042 s, range 0.118456500 to 0.121716458 s. The source-bound generated MEASUREMENT.json records every sample. Process startup, imports, source authentication and all scientific work are timed. Separate profiling identifies repeated determinant work; unchanged arithmetic and certificate checks limit the full gain.

Normal and optimized local checks pass, timed at 0.442819 s and 0.455167 s. They preserve all 19,654 actual determinant requests and the original complete caller, with exact ordered transcript equality. Additional evidence covers 154 schedules, 1,248 explicit conformance values, six rejecting controls and five actual source corruptions per mode. Registered replay, committed bytes/modes and declared source history pass. Official export integrity and both read-only Git-free empty-PATH replays pass, leaving all sixteen exported files and modes unchanged.

From the worktree root, using CPython 3.12 and the standard library:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/signed-leibniz-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/signed-leibniz-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/signed-leibniz-replay
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/signed-leibniz-replay --check-source-history
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/signed-leibniz-replay/benchmark.py --output /absolute/scratch/fresh-measurement.json

A different CPython 3.12 path may replace the local interpreter. Both registered checks have 120-second limits. Timing is descriptive and never gates CI.

Limitations

The exact evaluator is scoped to square integer or rational matrices through size five; the complete pinned caller stays inside that domain. This is one fixed caller on one host under shared load. It does not audit the predecessor capacity theorem, admit physical channels, supply native maps or change the selected frontier. The complete supplier/caller/precision/storage and all five framework assumptions retain their status. Selected cold replay, Lean, Docker, independent human review and formal proof-kernel review are unrun or unclaimed.

Open next questions

Can another complete source caller use the same fixed schedules without reducing its determinant domain? First profile that distinct caller and derive its dimension and arithmetic contracts. Broader performance and larger-dimension resource bounds are not supplied here.

Related open work

• Record one non-unit dyadic handoff that splits a rank-9 helper. #6297 constructs one nonunit dyadic physical helper handoff using the PR5611 completion compiler. This contribution only speeds the fixed PR5615 capacity replay and computes no new handoff invoice or channel count. No numerical comparison of that construction was made.
• No open PR targeting this complete verifier's runtime was found in the refreshed overlap checks. Other current replay optimizations use different callers and arithmetic kernels.

The completion refresh inspected all fifteen open account PRs created since the advance CLAIM, including this PR. None of the other fourteen targets this fixed PR5615 verifier or computes its complete-command runtime. No shared-instance numerical disagreement was found, and no extra computations were run to check another contribution.

CI notes

Both hosted checks, plan and replay (research/signed-leibniz-replay), passed at exact head dbdc3c4d82d9bb5d86e61122646d108c303439dc in Registered research packages run 41107351171. The completed checks were read once; separate run metadata confirms completed status, success and the matching head. The hosted replay runs both registered warning-strict normal and optimized commands.

All local direct, registered, committed-byte/source-history and read-only export checks listed above also pass. Hosted CI certifies execution of the declared finite checks and controls. The runtime percentage remains local measurement evidence; independent human and formal proof-kernel review are unclaimed.

Merge danger

Two-way door. Blast radius: this opt-in research package. Shared commands and predecessor sources are unchanged.

Advance claim.