[petalas]

Summary

A prepared finite-field row-update table reduces the complete PR5637 extension-field tensor-recognition caller's median wall time by 16.56%, from 13.202941292 to 11.016213791 seconds across five alternating fresh-process pairs. All ten processes succeed with identical deterministic output hashes and zero errors. The original range is 12.879240000 to 14.055809667 s; the prepared range is 10.861282875 to 11.409663292 s. Measurements include all preparation, imports, authentication, orbit traversal and certificate checks on CPython 3.12.15 / macOS arm64. Local contention and host differences remain relevant.

Claim type: scoped implementation-equivalence proof with finite conformance evidence and a local performance measurement. No new kappa, tensor classification or supplier admission is claimed.

unchanged complete caller
  -> private field preparation and exact row kernel
  -> unchanged decisions, transporter checks and orbit oracle

Only research/extension-field-row-kernel/ is added. Frozen predecessor bytes and the selected frontier remain unchanged. The new implementation, proof and experiment were produced by Nick Petalas. Credit Ali Romman / PR5637 for the finite-field arithmetic, recognizer, complete caller and semilinear proof; apoursh / PR5502 for the height criterion; PR5540/5525/5252 for reconstruction; PR5459 for characters; David Ganz and the retained predecessors. Table-driven finite-field elimination is classical.

Evidence and reproduction

The proof establishes exact equality of every returned row and ordered pivot column, including augmented columns. The new verifier passes 19,753 row-result comparisons, 21,061 fused arithmetic entries and 65 malformed-input, capacity and arithmetic-mutation controls. Both complete callers preserve all 256 F2 and 65,536 F4 tensors, 90 changed-basis presentations, 90 special-linear transporters, 2,322 basis products and 125 source controls. The nondeterministic elapsed-time line alone is excluded from report comparison.

Local warning-strict normal and optimized direct checks and both registered commands pass. Individually timed registered commands take 24.099 s and 25.834 s, below their 150-second bounds. Metadata and committed-byte/source-history checks pass at bcaee9ecd60195683a2d13bbb1762612ea4cde40. The official export and all six declared inputs pass integrity checking. Both read-only Git-free replay modes pass with empty PATH, and all sixteen exported files retain their bytes and read-only modes. Twelve actual source-corruption runs and two semantic-corruption runs reject in normal and optimized Python. Exact pins and all benchmark samples are in the package. Generated hash-bound receipts and replay logs are kept outside the checkout.

From the repository root, standard library only:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -X dev -B research/extension-field-row-kernel/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -X dev -B research/extension-field-row-kernel/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/extension-field-row-kernel
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/extension-field-row-kernel --check-source-history
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/extension-field-row-kernel/benchmark.py --pairs 5

Another CPython 3.12 path may replace the displayed interpreter. Expected markers are PASS_EXTENSION_FIELD_ROW_KERNEL, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. The five-pair benchmark is opt-in; CI asserts coverage and equivalence, without a machine-dependent speed threshold.

Limitations and unrun obligations

The adapter covers canonical unmodified field tables of order at most 25, at most 729 rows and at most 162 columns, including the complete retained caller. Larger fields/dimensions, mutation after preparation and transfer to other recognizers are outside the claim. Each field owns its own immutable arithmetic table; no cross-presentation cache is shared.

No native producer/consumer, complete paid supplier invoice, selected cold replay, Lean or Docker run is supplied. All five selected framework assumptions remain. Independent human and formal proof-kernel review are unclaimed. No local check was deferred solely to CI.

Open next questions

Can this bounded engine enter a source-owned recognition API with explicit field and augmented-row capacities? First specify that public contract while preserving exact full rows and pivot order. This package supplies a private adapter and keeps the source frozen; it does not reserve another optimization round.

Related open work

• Remove 7,982,993 raw-pencil product terms (no κ) #6309 reduces finite-field matrix-product work in the separate PR5692 raw-pencil caller, using retained PR5637 arithmetic. This PR changes row elimination in the PR5637 tensor recognizer. The kernels, workloads and measured quantities differ; no work-count or timing transfer is claimed.
• Reduce complete Frobenius recognition caller time by 65.44% (no κ) #6310 reduces associativity contractions in the PR5502 prime-field Frobenius recognizer. It shares recognition lineage with PR5637 but changes a different kernel and complete caller. No same-instance timing or classification number is compared.
• Skip 113,164 redundant modular products in stage-pair replay (no κ) #6313 omits redundant modular products in the historical h=6 stage-pair rank caller over prime 101. This is adjacent exact-elimination work with different matrices, field and caller; its arithmetic counts do not transfer to this bounded extension-field engine.

Completion refresh inspected all sixteen open account PRs created since the CLAIM, including this PR. The related lines above cover the recognition/arithmetic neighbors; none targets this exact complete caller or reports its runtime. The remaining contributions use different objects or workloads. No shared-instance numerical disagreement was identified, and no extra computations checked another contribution.

Merged #5661/#5664 and #5656/#5663/#5668 extend the mathematical recognition/character interfaces. No automatic implementation or timing transfer is claimed, and their scientific results were not recomputed for comparison.

CI notes

Both hosted checks passed at head bcaee9ecd60195683a2d13bbb1762612ea4cde40 in Registered research packages run 41106703644: plan in 4m14s and replay (research/extension-field-row-kernel) in 3m38s. The completed checks were read once. Separate run metadata confirms completed status, success and the matching head SHA. Hosted replay executes both registered normal and optimized commands.

All local direct, registered, committed-byte/source-history and portable-export checks listed above also passed. Hosted success certifies the bounded replay and controls; the timing improvement remains local evidence without a CI speed threshold. Independent human and formal proof-kernel review are unclaimed. All five selected framework assumptions retain their status.

Merge danger

Door: two-way. Blast radius: isolated package. Nine new files and an opt-in replay, with no shared-code or selected-frontier change.