[petalas]

Summary

The complete P104 span-fact command has a 67.09% lower local median wall time, 2.596 to 0.855 seconds. Its scalar and bitset ranges, 2.437–2.918 and 0.832–0.873 seconds, are separated. Claim type: measured verifier improvement with a scoped implementation-equivalence proof and finite exact conformance. No new mathematical bound or kappa is claimed.

The enclosing bounded B-form verifier has an observed 8.79% lower median, 14.982 to 13.665 seconds. Its whole-caller wall-time comparison is inconclusive because its ranges overlap and host variation exceeds that median difference. The complete caller comparison and every raw sample remain in the package.

- recompute scalar port parity inside every section-pair count
+ compute each parity section once, then intersect integer bitsets

Every one of the 130,305 P104 section pairs remains. The source-bound adapter retains the enclosing verifier's other subprocesses, assertions, recorded-log authentication, result comparisons and controls. Only research/p104-span-bitset/ is added. Predecessor files and the selected frontier are unchanged.

Package at the contribution head · Advance CLAIM

Evidence

Before: profiling identifies repeated scalar label parity as the dominant span-command cost. After: five alternating fresh-process pairs for each complete command give twenty matching normalized outputs and zero errors. All five enclosing-verifier pairs favor the bitset version. Complete-command ranges are 14.120–16.949 seconds versus 13.123–14.272 seconds. They overlap; the exact descriptive rank-sum tail is 8/252, two-sided p=0.031746. The whole-caller comparison remains inconclusive despite that descriptive test. The span-command percentage is a single-host observation under recorded background load, not a portable guarantee.

BENCHMARK.json contains every timing, transcript hash and implementation/input binding. STATISTICS.json binds its descriptive calculation to that record. The equivalence argument is in PROOF.md. Measurements use CPython 3.12.15, macOS arm64, 18 logical CPUs and numpy 2.5.4. Both compared engines use the same environment; no cross-version speed claim is made.

• Warning-strict normal and optimized direct checks pass in 30.866 and 31.334 seconds. These are the two registered command shapes, both below their 180-second limits.
• All 281 fixtures, 136,569 section pairs and sixteen domain/source/section/record controls pass. Normal child execution preserves predecessor assertions under an optimized conformance parent.
• Both registered checks pass with PASS_REGISTERED_RESEARCH_PACKAGE.
• Committed bytes, executable modes and source ancestry pass for 116 files at ab4f7b56bc152d29afa2c40062b29f2c5a9e5cfc.
• Official export integrity and all 105 declared-input coverage checks pass. Both modes pass from a read-only Git-free export with an empty executable search path; all 117 exported regular files retain their bytes and modes.

From the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/p104-span-bitset/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -O -B research/p104-span-bitset/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/p104-span-bitset
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/p104-span-bitset --check-source-history --check-modes
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B research/p104-span-bitset/benchmark.py

The last command generates fresh timing JSON on stdout. Another CPython 3.12 path may replace the local path. The manifest pins numpy 2.5.4. For the faster consumer alone, use replay.py --scope complete --engine bitset with the same interpreter.

Limitations and unrun obligations

This preserves the predecessor's bounded coverage. Its full historical census and Lean build remain unrun; authenticating recorded logs does not recompute that census. This is not an audit or independent acceptance of the predecessor mathematics. A stable checkout and the exact pinned inputs are required. Physical/native/caller admission, the selected cold replay and the complete multiplication theorem are outside scope. Independent human and formal proof-kernel review are unclaimed.

Related open work

Completion refresh found no currently open account PR created since the advance CLAIM at 2026-10-29 22:09:12 UTC. No new same-command numerical comparison was required; no additional predecessor computations were run.

• PR6204 improves the offline archive checker, a different complete command and workload. It predates this CLAIM.
• PR6247 constructs a dyadic rank-seven P104 projector on the shared root geometry. It supplies no timing for this span-fact command, so no numerical comparison is made.
• PR6248 proves a two-cache tariff for reader 497 on a P104 word. Its paid-cost quantity differs from the present replay runtime.

The previously listed PR6218, PR6198, PR6217, PR6219, PR6221 and PR6227 have merged. They remain related mathematical context rather than open competing work. Their proofs, root geometry and quantities are not newly audited here; the predecessor credit above and below is retained.

Open next questions

Can the incidence representation help another explicit finite-fact consumer? Start with a profile of a different complete command and declare its full output and checks before adapting it. No other consumer or remaining B-form replay stage is optimized here.

Credit

Matarener retains PR6188's mathematics, root model, finite domains, original verifier and recorded evidence. DreamingOfClouds retains the underlying nine-term decoder/geometry code and credited predecessor lineage. The incidence implementation, source adapter, equivalence argument and measurements are produced by Nick Petalas. Bitset intersection and population count are standard methods; no literature-priority claim is made. Apache-2.0.

CI notes

Both hosted checks, plan and replay (research/p104-span-bitset), passed at exact head ab4f7b56bc152d29afa2c40062b29f2c5a9e5cfc in run 40965973865. The completed checks were read once; the run's successful conclusion and exact head were confirmed. A maintainer subsequently merged this PR.

Hosted replay certifies the registered package conformance at this head. The local timing percentage is not a CI performance assertion. The local normal/optimized replay, committed-byte/mode/source-history and read-only Git-free export checks listed above also passed. Full historical census, Lean, selected cold replay, independent human review and formal proof-kernel acceptance remain unclaimed. No CI failure remains to report.

Merge Danger

Door: two-way.

Blast Radius: research.

The optional implementation and its evidence occupy one new package. Existing implementations, frozen inputs and selected records are unchanged.