[petalas]

Summary

The complete PR3806 primary chirp-residue replay runs 19.30% faster by median wall time, from 2.4564 s to 1.9822 s across five alternating fresh-process pairs. All ten outputs match, with zero errors. This is a bounded implementation improvement with a scoped equivalence proof, not a new chirp theorem or kappa.

 at each one-axis state
-  require(predicate, label)
+  if not predicate: raise the same failure

The isolated adapter keeps all 13,981,010 one-axis states, 6,141 rollouts, 21,840 two-axis states, 4,096 square checks, 3,905 visit tuples and original receipt comparisons. It eliminates exactly 41,955,312 successful condition-call boundaries. Frozen sources and the selected frontier are unchanged.

Credit James Reed / jwr404's PR3806 for the replay and mathematical result, Jose Manuel / PR3763 for the producer, Chafik Boukhalfa for the residue schedule, and Ross Richardson for the symbolic-transition lineage. This contribution was produced by Nick Petalas.

Evidence

At exact head f11d40da4723e01cc3689dd698497972202aafc7:

• Complete baseline/fast stdout and all ordered rollout tuples agree. The new verifier rejects all 1,533 corrupted small initial states, fifteen malformed domain/control states and a changed source before execution. The original independent test runs unchanged in a nonoptimized child.
• Both warning-strict registered commands and their direct normal/optimized executions pass. Direct durations are 4.204 s and 4.196 s, below each 120-second limit.
• Metadata/pins pass. All fifteen committed package/input files pass byte, executable-mode and declared source-history checks against canonical base 7c49fe32c55de02c2c873655c804b16e4c3fef0a.
• Generated BENCHMARK.json preserves all samples, exact source hashes and host/interpreter data. Baseline range is 2.4403–2.4750 s; fast range is 1.9595–2.0033 s, on shared macOS arm64 / CPython 3.12.15 with eighteen logical cores. Separate profiles locate the bottleneck and corroborate the removed-call count. Instrumented times are excluded from the speed measurement.

From the worktree root, using the standard library:

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

Any CPython 3.12 interpreter may replace the absolute path. The markers are PASS_CHIRP_RESIDUE_LOOP, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. To repeat timing, choose a fresh path outside the checkout:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/chirp-residue-loop/benchmark.py --output /absolute/scratch/benchmark.json

Limitations and unrun obligations

The timing covers the complete primary source command plus identical authentication wrappers. The separate independent test and new conformance harness are checked outside that timing. The loop accepts only the retained driver's radius 4..4096, its two flag lengths and admitted odd slopes. Cross-platform performance and an unrestricted API replacement are unclaimed.

No physical-consumer speedup, native implementation, supplier invoice, precision/storage/ownership/compiler or outer-admission result is supplied. All five selected framework assumptions remain. No selected cold replay, Lean, Docker, independent human or formal proof-kernel review ran. No required local package check is deferred to CI.

Open next questions

• Can remaining closed-form arithmetic be reduced while keeping a separate predicate at every state? Start with the final fast profile, prove preserved coverage and measure the full command.
• Does a named physical chirp consumer actually call this loop and benefit? Identify its complete execution and paid costs first; no such consumer comparison is supplied.

Related open work

No other open PR was found studying the PR3806 replay or its one-axis loop in the refreshed object/source searches.

• PR6482 concerns a separate Gaussian product-residue packing lane. This package computes no shared packing-size or precision quantity, and no extra computations checked that contribution.

Closeout inspected the eleven other open account PRs created since the CLAIM: #6591, #6592, #6593, #6594, #6595, #6596, #6597, #6598, #6600, #6601 and #6602. None studies the PR3806 one-axis loop or computes a shared result. No extra computations checked those contributions.

• PR6598 optimizes the separate PR1212 rank-eight RUP replay, with a different source, input, checks and timing workload.

The replay-runtime card is refined to this source-bound complete command. The advance claim, live reservations, current main/merged searches and cached coverage are recorded in TASK.json. Sparse notes, arbitrary historical diffs and unpublished work remain search limits.

CI notes

Both hosted checks passed at exact head f11d40da4723e01cc3689dd698497972202aafc7 in run 41626264108: plan and replay (research/chirp-residue-loop). One checks read confirmed both successes; run metadata confirms completed success at this same head. Both bounded registered scientific commands and all required local publication checks passed. Timing is not a CI gate; hosted success certifies the bounded checks and bindings, without establishing a new chirp theorem or complete multiplication theorem.

Merge Danger

Door: two-way.

Blast Radius: isolated.

Only research/chirp-residue-loop is added. No shared implementation, frozen predecessor, upstream source or selected-frontier file changes.