[petalas]

Summary

Add a guarded packed implementation of P104 Gaussian Newton membership. This is a scoped algorithm-preservation proof with finite corroboration and local performance evidence, produced by Nick Petalas.

validated Gaussian pairs -> bounded residues in byte lanes
                        -> one guarded subtraction per address bit
                        -> identical first-failure certificate

At rank nine, the transform uses nine packed integer subtractions in place of 4,608 component subtractions. These operations have different widths; their count ratio is not a runtime or bit-complexity claim. The complete public call takes 45.35% less median time on one accepted fixture. Complete-replay timing is inconclusive.

Credit Ali Romman/PR5374 for bounded-residue validation and Clear1nsight/PR3382 for the Gaussian Newton lattice, with ywz65, Arham Tahir, Tekalign/PR3025, Ross Richardson and the retained collector, word, wrapper and period-domain lineage. Their mathematical results are cited premises, not audit deliverables. The new result is the packed implementation, preservation proof and opt-in source replay adapter. General guarded arithmetic and Boolean transforms are standard techniques.

Evidence

• Exact checker: PASS_PACKED_NEWTON_MEMBERSHIP, with 1,364 digit-pair cases, 65,812 small arrays, 160 broad signed/boundary fixtures, independent subset-sum coefficient checks and 13 rejection/fault controls. The complete inherited replay executes unchanged independent oracles and all 96 collector prefixes, returning the identical recorded result.
• Warning-strict normal and optimized registered commands both pass locally and each took 1.14 seconds when timed directly. Development-mode checks, source compilation, function-size bounds, tabnanny and whitespace checks pass.
• Committed bytes, executable modes and source ancestry pass for all 20 package/input files at 4195c5cb137ecdd655ca564d404b6d62a5d5245f. No required local check is deferred to CI.
• Five alternating fresh-process trials per side, 1,000 complete accepted calls per trial, zero errors. API medians: 0.290105 to 0.158548 seconds per 1,000 calls; ranges 0.271077–0.366769 and 0.147782–0.162996. Actual input components reach 1,034 bits. Complete replay medians fall from 0.907932 to 0.859743 seconds, but the ranges overlap and observed variation exceeds the gap, so no complete-replay speedup is claimed. PERFORMANCE.md records the limiter, full-process costs and environment; the benchmark prints raw samples and controlling-file hashes.

Reproduce from the repository root with standard-library CPython 3.12. Substitute another CPython 3.12 path on another host.

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

Limitations and unrun obligations

Exact preservation is proved for ranks 0 through 9 and absolute component bit lengths at most 8,192. Outside this declared domain the new API rejects; it does not replace the unbounded reference. It emits no decoded wide coefficients and patches no shared default caller.

No physical validation scan, allocation/erasure/restoration tariff, native realization, compiler closure, supplier admission or multiplication theorem is established. All five selected framework assumptions remain. No new kappa or selected-frontier change. No selected cold replay, Lean, Docker, independent human review or formal proof-kernel acceptance is claimed. Timing is local, fixture-specific evidence.

Open next questions

• Can an actual membership-only physical consumer benefit after input acquisition, movement and restoration are charged? First name and price one complete consumer.
• Can the unchanged validation/independent-decoder work in a complete replay be reduced without losing its diagnostics? First profile one distinct source-bound replacement.

Related open work

• PR6478 prices per-addition precision in a Gaussian Newton graph; this package changes exact bounded-residue membership arithmetic and computes no shared precision optimum.
• PR6482 changes a Gaussian residue convolution lane using centered packing; this package packs Boolean differences for a different predicate and computes no residue-child width or shared numerical value.
• PR6505 changes complete P104 root-certificate checking; this package changes the entrance membership predicate, not a root or invoice.

Live claims, open/account lists, complete cached open-PR coverage and source-specific main/merged searches were checked before committing. Sparse cached notes, unpublished work and arbitrary diffs remain outside coverage. PR5374 is the merged predecessor. No extra computations were run to check related results.

The completion refresh inspected all eight account PRs still open and created since the advance CLAIM at 2026-11-03 18:15:19Z, including this PR. The seven others concern the fixed F4 decoder, a translated Gaussian reader basis, P104 opening preparation, clean-checkpoint trees, Dic3 replay, non-Frobenius tensor characters and mirror-window construction. None studies this bounded Gaussian Newton membership transform or reports a shared computed quantity. No additional related-work line or numerical comparison is needed; no extra computations were run to audit their results.

CI notes

Hosted CI did not certify head 4195c5cb137ecdd655ca564d404b6d62a5d5245f. Run 41693750102, plan job, was cancelled by the workflow's 10-minute timeout while still in actions/checkout. The job ran from 2026-11-03 18:25:59Z to 18:36:04Z; checkout was cancelled at 18:36:01Z. Python setup, onboarding tests and package selection were skipped, and the package replay job was skipped. This is a checkout infrastructure timeout, not a package-test failure.

The same checkout-stage timeout is recorded in concurrent run 41694097281 and run 41695104695. Their job/step metadata was checked; no scientific result is inferred from those cancellations.

Validation is local only: both registered normal/optimized commands, direct warning-strict and development-mode checks, complete inherited replay preservation, independent coefficient and failure controls, source compilation/function bounds/tabnanny, whitespace, and committed-byte/mode/source-history checks listed in Evidence passed. Hosted CI certified none of these checks for this head. Local preservation evidence is not independent scientific or proof-kernel acceptance.

Merge danger

Door: two-way. Blast radius: package. Ten new isolated research files; frozen predecessor evidence and the selected construction are unchanged.