[petalas]

Summary

The complete retained PR3166 scientific replay takes 13.95% less median wall time locally, from 6.131 s to 5.275 s across five alternating fresh-process pairs. All ten runs pass with identical scientific stdout and no stderr. Claim type: scoped implementation-equivalence proof, exact finite conformance and local performance evidence. The E8 mathematical results remain conorholds's contribution. No new kappa or selected-frontier change is claimed.

authenticate ten unchanged scientific inputs
  load four original source modules
  specialize two exact eight-coordinate dot products
  execute original main and complete certificate comparison

This contribution was produced by Nick Petalas. Credit conorholds / PR3166 for the complete original replay, proofs, checks and certificates, and DreamingOfClouds / PR2816, PR2826, PR2862 and PR3154 with the retained E8 lineage. Fixed-product unrolling is standard. The new contribution is its source-bound implementation, preservation argument and measured complete consumer. PR6164 previously optimized publication-byte preflight using this fixture; it did not accelerate this scientific command. Advance CLAIM.

Evidence

Before: the pinned default scientific command uses generator/sum dot products. After: the opt-in adapter replaces only those two functions, keeping the independent Cartan implementation, Gaussian algebra, geometry, rejection controls, source hashes and original complete RESULT.json comparison.

• All 5,096,623 replaced calls agree exactly with their original function in a full conformance execution. All 576 scalar fixtures and nineteen domain, physical source-byte, missing-input and actual wrong-kernel controls pass.
• Both warning-strict normal and optimized registered commands pass locally, timed separately at 6.915 s and 7.076 s, below their 120-second limits. The direct verifier and package metadata/replay pass. Generated receipts agree and bind all eight package files.
• Five alternating original/candidate process pairs have zero failures. Median times are 6.130820 s and 5.275435 s; ranges are 6.083976 to 6.376638 s and 5.110564 to 5.607583 s. Every candidate run is faster. README.md retains every timing pair. A separate profile identifies the two dot functions as 20.8% of the instrumented run, consistent with the measured complete saving.
• CPython 3.12.15, macOS 27.0.1 arm64, 18 logical CPUs. The host is shared; initial load averages were 2.27, 2.58, 1.99. Timing includes startup, imports, arithmetic, all checks and output capture. No other replay from this contribution ran during measurement.
• Committed bytes and source history pass for eighteen package/input files at de49f92361c0b392cf30a9a79b7fa8b83cc90ca9. Official export integrity passes. Optimized read-only, Git-free execution with an empty executable PATH passes with the same generated receipt; all nineteen exported files retain their bytes and modes.

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

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/e8-root-swap-fast-inner/replay.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/e8-root-swap-fast-inner/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -O -B research/e8-root-swap-fast-inner/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/e8-root-swap-fast-inner/benchmark.py --pairs 5
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/e8-root-swap-fast-inner
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/e8-root-swap-fast-inner --check-source-history

Another local CPython 3.12 executable can replace the absolute path. Set TMPDIR to a private external directory for temporary controls. Direct conformance emits PASS_E8_ROOT_SWAP_FAST_INNER; registered replay emits PASS_REGISTERED_RESEARCH_PACKAGE. Benchmark evidence is generated stdout, with all command lines, nanoseconds, output digests, return codes and the failure count.

Limitations and unrun obligations

The performance result is local to this complete historical fixture and host. The substitution proof covers exact integer/rational eight-coordinate calls and the pinned default source command. Arbitrary overloaded scalar types, original receipt-emission options, arbitrary module-cache states and future source changes are excluded. No independent mathematical audit or general literature-priority claim is made. Lean bytes are authenticated but Lean is not run. No physical caller, supplier admission, precision, tape, stock, compiler, outer or selected cold replay is supplied. All five selected framework assumptions remain. Independent human and formal proof-kernel review are unclaimed. No registered local obligation remains unrun. Hosted replay also passed at the publication head; independent mathematical acceptance remains unclaimed.

Open next questions

• Integrate the specialization into one maintained replay consumer while retaining intended arithmetic independence. First identify that consumer and measure its complete command. No such integration is supplied here.
• Profile that consumer's remaining bottleneck before another optimization. This contribution stops at its first verified improvement and reserves no follow-up.

Related open work

• PR6570 accelerates the complete PR1668 binary-incidence replay by removing zero products. This PR accelerates the separate complete PR3166 replay with an eight-coordinate dot specialization. The timings concern different workloads and are not competing numerical estimates.

The completion refresh listed all 112 account open PRs and inspected the fifteen created since the advance CLAIM at 2026-11-03T09:10:38Z, including this one. The fourteen others are #6556 through #6568 and #6570. None studies this exact default scientific command or reports a conflicting value for its runtime or conformance counts. No extra scientific computation audited another contribution.

The earlier complete cached 506-PR corpus, refreshed live list and targeted merged/main searches found no other open PR changing this exact command. PR3166 and publication-byte optimization PR6164 are merged predecessors. Sparse local notes, arbitrary historical diffs and unpublished work remain coverage limits.

CI notes

Both hosted checks passed at exact head de49f92361c0b392cf30a9a79b7fa8b83cc90ca9 in Registered research packages run 41610563780: plan in 4m26s and replay (research/e8-root-swap-fast-inner) in 2m1s. The completed checks were read once. Run metadata confirms the matching head, completed status and successful conclusion.

Hosted replay executes both registered warning-strict normal and optimized conformance commands. Local package metadata/pins, direct and registered checks, committed bytes/source history and read-only Git-free export also pass. CI certifies execution of the bounded checks and source metadata, not the local timing percentage or independent acceptance of the predecessor's mathematical proofs. No hosted check failed and no registered obligation remains unrun.

Merge danger

Door: two-way.

Blast radius: isolated.

Eight new files in one opt-in package and ten declared read-only inputs. Shared code, frozen sources, predecessor credit and selected-frontier records are unchanged.