[petalas]

Summary

The complete composed PR5221 scientific replay has a 33.75% lower median local runtime with identical output. Claim type: scoped implementation-equivalence proof, exact finite conformance and a measured replay-time improvement. No new mathematical repair rank or kappa.

 rank-only Gaussian evaluator
- reduce every pivot column above and below the pivot
+ eliminate below each pivot and update only its remaining row suffix
 both complete primary and independent scientific bodies retained

The optional seven-file package is research/quinary-forward-rank/. It authenticates six source inputs, changes exactly one function binding, and retains the complete primary main block, independent body, typed receipt, fixtures and rejection controls. Both source bodies run sequentially in one fresh process in each timed mode. This measures the complete composed scientific consumer; shared package-runner/CI planning costs and two separate interpreter startups are outside the measurement.

Produced by Nick Petalas. Credit Brian / JoyboyBrian PR5221 for the full repair law and both scientific consumers, with Ali Romman PR4962, Nick Petalas PR5173, mikey1201 PR172, icekylinx PR144 and the retained tensor/deletion lineage. Gaussian elimination is classical; the source-bound implementation and complete-consumer evidence are the new contribution. No predecessor mathematical claim is being audited.

Advance CLAIM. Base and submission refresh are canonical main 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8, selected PR6030.

Evidence

• Before: median 0.283317125 s, range [0.282368625, 0.288796625]. After: median 0.187691209 s, range [0.184945250, 0.194998125]. Five alternating fresh-process pairs per side, zero errors and exact complete stdout equality. The ranges do not overlap. CPython 3.12.15, macOS 27.0.1 arm64, 18 logical CPUs, with other processes present. Raw pairs and execution boundaries are in README.md. An untimed profile places 0.209 of 0.242 primary seconds in row reduction. This is local fixed-consumer evidence, not a portable speed guarantee.
• All 28 reached rank calls agree with the original and preserve their input matrices. Every one of the 15,625 F5 two-by-three matrices agrees with a separate minor oracle; rank histogram [1,744,14880]. Another 89 boundary cases and eleven rejecting controls pass.
• Warning-strict normal and optimized direct and registered checks pass. Final direct commands took 0.613 s and 0.812 s, below their 120-second limits. These are check durations, not benchmark samples. No scoped registered command is left solely to CI.
• At head e72837b58f04bbbb7414402062a2f8db3e3a0b0f, committed bytes, modes and full source-history preflight pass for thirteen package/input files. Official export integrity and declared-input checks pass. Normal and optimized read-only Git-free replay pass with empty PATH; all fourteen exported files remain byte-identical. An actual mutated exported source is rejected before execution.
• Every direct run generates a receipt bound to all seven package files and six live inputs. No scientific receipt is handwritten. Source compilation, function-size inspection and staged whitespace checks pass.

From the repository root, standard library only:

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

Any CPython 3.12 installation may replace the displayed interpreter. Expected markers are PASS_QUINARY_FORWARD_RANK, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. README.md gives the complete measurement command with an external exclusive output path.

Limitations and unrun obligations

The evaluator is rank-only over F5, at most 256 rows and columns and 64-bit integer inputs. Its written equivalence proof is outside a formal kernel. The independent command is retained without optimization. Default adoption and historical source-pin migration are not implemented. This adds one isolated optional package; predecessor files and the selected frontier are unchanged.

Native maps, physical callers, ownership/restoration, routing, precision/tape, stock, compiler and outer admission remain outside scope. Lean, Docker, heavy native builds and the selected scientific cold replay were not run. Independent human and formal proof-kernel review are unclaimed. No complete multiplication theorem or new kappa is supplied.

Open next questions

Can the evaluator be adopted in the default consumer while preserving historical source pins? First specify the migration and retain both full scientific bodies and the typed receipt. Default integration is missing; no further optimization is reserved.

Related open work

No other open PR studying the PR5221 characteristic-five consumer or its rank evaluator appeared in the complete-pagination cached scan, live topic searches, refreshed open list or recent claims. PR5221 is the merged predecessor. The earlier PR6135 DisjointTensor serialization optimization has a different compiler, consumer and representation; this contribution is not its follow-up. Sparse historical notes, arbitrary diffs and unpublished work remain coverage limits. No extra computations were run to compare other contributors' mathematical results.

• PR6460 reduces complete nilpotent-Schur replay time through bounded matrix-product reuse. Its consumer and workload differ from this characteristic-five rank evaluator; no timing or mathematical value is compared across the consumers.
• PR6466 reduces observable-mask planner preparation time using a hypercube transform. It evaluates a different recurrence and consumer, with no common numerical endpoint computed here.

The completion refresh inspected all thirteen account open PRs created since the advance CLAIM, including this PR (#6459 through #6471). The twelve others study distinct objects or consumers; none was found to study this PR5221 rank evaluator or report a conflicting common-instance value. The two adjacent runtime submissions are listed above. No additional computations checked another contribution.

CI notes

Both hosted checks passed at exact head e72837b58f04bbbb7414402062a2f8db3e3a0b0f in run 41551184139: plan in 4m29s and replay (research/quinary-forward-rank) in 1m19s. The completed checks were read once; run metadata confirms completed status, success and the matching head.

Hosted replay passed the registered warning-strict normal and optimized conformance commands and source metadata checks. All direct and registered local checks, committed-byte/source-history/mode preflights and read-only Git-free export checks also pass. The timing experiment remains local evidence; CI does not measure a portable speedup or establish independent scientific acceptance of the written equivalence argument. No hosted failure remains to report.

Merge Danger

Door: two-way. Blast radius: isolated. Seven new files in one optional research package; no shared code, frozen predecessor, pinned evidence or selected record is modified. Archival merge and scientific acceptance remain separate.