[petalas]

Summary

The complete PR3773 scientific consumer takes 79.02% less median wall time locally, from 0.654020 s to 0.137189 s. A packed Gray-code enumerator replaces repeated parity evaluation while retaining every core, section and scientific check. Only research/core-section-gray-replay/ is added.

for each of 3,780 cores
  pack its seven coordinate columns
  visit all 127 nonzero masks by one-column XOR updates
  run the original histogram, aggregate and result checks

Claim type: scoped implementation-equivalence proof, exact finite conformance and local performance evidence. This contribution was produced by Nick Petalas. Credit James Reed / jwr404's PR3773 at 83cb934664879552405c60987ceca100f9656a49 for the complete consumer and published histogram, conorholds for the recorded premise, Nick Petalas for the retained E8 geometry, and the original P112 lineage. Gray-code enumeration and packed binary columns are classical. The predecessor's mathematical result is a cited input, not an audit deliverable or new claim. No new kappa or selected-frontier change.

Evidence

• Before: 11,521,440 mask/coordinate parity evaluations in the fixed complete consumer. After: 635,040 column bit tests and 480,060 packed XOR updates, with every nonzero-mask section retained. The written invariant proves exact per-mask equality; one unique expression is replaced in authenticated private source, with every other source byte retained.
• All 480,060 reached nonzero-mask sections agree with direct evaluation. Exhaustive small-list checks cover 5,058 lists and 74,958 mask entries, plus all 1,024 masks at the API capacity boundary. Seventeen input/source invalidation controls and six scientific mutation controls reject for their expected reasons.
• Five alternating fresh-process pairs have identical full stdout, empty stderr and zero failures. Original seconds: 0.654254, 0.652888, 0.654020, 0.660023, 0.653303. Gray seconds: 0.139853, 0.137321, 0.135996, 0.137189, 0.136774. The ranges do not overlap. A separate profile identifies section construction/Counter accumulation as the limiter. The timed scope includes startup, authentication and the complete scientific main; metadata validation, added conformance and the predecessor's arithmetic-only test script are separate.
• Local host: CPython 3.12.15, macOS 27.0.1 arm64, 18 logical CPUs, shared load around 1.66. Timing is local evidence, not a portable guarantee. Measured replay/benchmark/source-manifest hashes still match the committed code.
• Warning-strict normal/optimized registered conformance and the uninstrumented fast consumer pass locally in 1.027 s, 0.815 s and 0.139 s. The registered runner, direct verifier, in-memory syntax diagnostics, diff checks and committed-byte/source-history preflight pass. The preflight covers eleven files at 272d21ebfa8bd77597a6ac3b6388c20c4dc02279. A generated verification receipt binds the final package hashes; no receipt is hand-written.

Reproduce from the repository root with CPython 3.12 and the standard library:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/core-section-gray-replay
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/core-section-gray-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/core-section-gray-replay/benchmark.py --pairs 5
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/core-section-gray-replay --check-source-history

Replace the interpreter path with another CPython 3.12 installation if needed. The verifier prints PASS_CORE_SECTION_GRAY_REPLAY; the uninstrumented consumer prints the unchanged PASS_CORE_SECTION_CAPACITY pairs=3780 sections=127 no_new_kappa.

Limitations and unrun obligations

The proof concerns the replacement, with executable limits of dimension ten and 256 coordinates. The predecessor geometry and histogram are retained premises. No independent predecessor audit, Linux performance measurement, proof-kernel build, Lean, Docker or selected supplier replay was run. Native execution, physical ownership/restoration, precision, stock, tape movement, complete supplier/outer invoices and all five selected framework assumptions remain outside this result. Independent human and formal proof-kernel review are unclaimed.

Related open work

No other open PR targeting the fixed PR3773 core-section consumer or its functional-section enumeration was found in the refreshed open list, complete cached open/Discussion coverage and targeted main/merged searches. Sparse notes, arbitrary historical diffs and unpublished work remain coverage limits. The completion refresh screened twelve other account open PRs created since the advance CLAIM. None supplies a competing value for this fixed section histogram or complete-command timing; the adjacent work below uses different objects or workloads.

• PR6569 optimizes a different E8 root-swap consumer; it does not enumerate these core sections. No shared timing comparison is claimed.
• PR6570 optimizes a frame-incidence consumer's kernel products; its workload and counts differ from this consumer. No shared numerical comparison is claimed.
• PR6579 prices a corrected E8 reader space using a character-kernel filtration. Its functional domain and quantity differ from this orthogonal-core section histogram.
• PR6582 classifies simultaneous A2 rank-six equality supports in the E8 label configuration. It computes a different incidence relation, with no shared numerical comparison here.
• PR6580 accelerates PR1624's paired26 certificate command with integer dot products. Its certificate, workload and complete-command timing differ from this consumer.
• PR6584 accelerates PR2061's A2+E6 primary replay by caching fixed rational contractions. It does not enumerate the orthogonal-core sections or report this consumer's runtime.

Open next questions

Should a maintained consumer adopt this enumerator? First review the one-expression substitution and reproduce the complete benchmark on one Linux host. Maintainer adoption and Linux performance evidence remain separate. Optimization stopped at the first verified improvement; no wider census is reserved.

CI notes

Both hosted checks, plan and replay (research/core-section-gray-replay), passed at commit 272d21ebfa8bd77597a6ac3b6388c20c4dc02279 in run 41618148690. The completed checks were read once; run metadata separately confirms the matching head, status completed and conclusion success. Planning took 4m33s and the registered replay job took 1m26s.

All three registered commands also passed locally. Hosted CI certifies the metadata and registered automated checks, including normal/optimized conformance and the uninstrumented fast scientific consumer. The timing percentage remains local evidence. CI does not independently accept the written equivalence proof, re-prove the predecessor theorem or discharge the five selected framework assumptions. No local obligation for this bounded adapter remains unrun.

Merge Danger

Door: two-way.

Blast radius: isolated. Eight new research-package files; source packages, shared implementations and the selected frontier are unchanged.