[petalas]

Summary

Scoped implementation-equivalence proof, exact operation-count certificate and local performance result. Cache fixed rational contractions in Adam Gall's complete PR2061 primary replay. Every scientific check, rejection control, ordered comparison and full result comparison remains.

- 156249 eight-coordinate contractions across two identity invocations
+   2016 eight-coordinate contractions

This removes 154,233 contractions and 1,233,864 rational multiplications. Five alternating fresh-process runs per side reduce the complete primary CLI's median elapsed time by 27.86%. The result was produced by Nick Petalas.

Credit Adam Gall / PR2061, exact head eed23989eddf7ec0b2c24d9e3794d0fca53f11ab, for the scientific workload, COPY69 theorem and controls; joaqcoo / PR1224 for the normal family and geometry; and the deficiency, decoder, coverage and ceiling contributors retained in that package. No predecessor theorem is claimed as new.

Evidence

At head 4817ce236389d707ab23f9f9f733c8535fb4d8b7:

• All ten timed processes succeeded, with identical stdout and empty stderr. Original median 2.354848833 seconds, range 2.331363334–2.602431125. Cached median 1.698670834 seconds, range 1.675971083–1.886004875. Exact nanosecond samples, load averages and the measurement boundary are retained in README.md.
• A separate profile attributes about 58% of original run time to the changed routine. The unchanged interval budget arithmetic limits the remaining runtime. Profiling is excluded from the timing sample.
• The verifier retains all 12,544 positive identity entries and the original coefficient mutation's rejection at entry 4,817. The complete fresh predecessor certificate equals its pinned RESULT.json.
• Both registered warning-strict checks passed locally, including 37 rational controls and ten source-admission controls. Direct normal and optimized commands took 1.673 and 1.932 seconds, respectively.
• Registered package metadata/source checks, exact committed bytes/source-history preflight, official 17-file export/integrity, AST compilation and staged whitespace checks pass. Normal and optimized read-only Git-free exported verification pass with identical receipts.

From the worktree root, reproduce with CPython 3.12 and its standard library:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/a2-e6-cached-contractions/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/a2-e6-cached-contractions/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/a2-e6-cached-contractions
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/a2-e6-cached-contractions --check-source-history
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/a2-e6-cached-contractions/benchmark.py

Another CPython 3.12 executable may replace the local absolute path. Set TMPDIR to an external scratch directory for the temporary corruption controls. Scientific receipts are generated on stdout and bind package-file hashes.

Limitations

The measured boundary is the complete primary CLI, including imports, source authentication, construction, scientific checks, certificate comparison and output. It is not the entire four-command predecessor workflow. Its independent checker and test driver are unchanged and unoptimized.

Measurements are local CPython 3.12.15 on macOS 27.0.1 arm64 under shared-machine load; no portable percentage is promised. Production adoption, whole-workflow Linux timing, selected cold replay, native admission, Lean and Docker are unrun. Independent human and formal proof-kernel review are unclaimed. The selected kappa and all five framework assumptions remain unchanged. No new decoder optimum, supplier or complete multiplication theorem is claimed.

Open next questions

Should this adapter be adopted by PR2061's registered workflow? Start with an explicit successor source binding and the complete four-command Linux replay. Default adoption and a whole-workflow measurement are the remaining obligations; they do not follow from a primary-CLI gain.

Related open work

The completion refresh covered this account's open PRs created since the advance CLAIM. No competing computation of this exact A2+E6 primary command, its runtime or its COPY69 certificate was found. PR2061 is the merged predecessor.

• PR6586 proves a sparse rank-one E6 correction invoice bound on a different fixed configuration. It does not evaluate this A2+E6 decoder or its COPY69 quantity.
• PR6583 accelerates PR3773's orthogonal-core section consumer using packed Gray updates. Its fixture, certificate and complete command differ; no cross-fixture timing comparison is asserted.
• PR6582 classifies simultaneous rank-six A2 equality supports in the full E8 label configuration. That incidence theorem does not compute this fixed P112 decoder certificate.
• PR6580 accelerates PR1624's paired26 primary command with mutation-aware rational-dot normalization. Its normal family, certificate and timed command differ from this contraction cache.
• PR6579 prices one corrected E8 reader basis. It neither changes nor evaluates the COPY69 decoder or this complete replay.

No extra mathematical computations were run to compare these contributions; no common newly computed numerical quantity was identified.

CI notes

Both hosted checks, plan and replay (research/a2-e6-cached-contractions), passed at exact head 4817ce236389d707ab23f9f9f733c8535fb4d8b7 in run 41618528553. The completed check list was read once. The current PR head matches that commit.

The registered replay executes the complete normal and optimized verification commands, including source authentication, full predecessor-certificate comparison and the added conformance controls. All registered commands also passed locally. Hosted CI certifies their execution; the 27.86% timing reduction remains local measurement evidence. Independent human and formal proof-kernel review, production adoption and the five selected framework assumptions remain unclaimed or unresolved as stated above.

Merge Danger

Door: two-way. Blast radius: isolated. Adds eight files in one opt-in package and leaves frozen sources and the selected frontier unchanged.