[petalas]

Summary

The complete PR1431 pivot-440 independent replay spends most of its time propagating donor pulses through fixed rational gates. Preparing each exact coefficient once reduces its local median wall time by 15.91%, from 5.886 s to 4.949 s, while retaining the complete caller and its saved mathematical receipt.

 complete independent caller
-  reconstruct a Fraction at every gate visit
+  prepare one exact Fraction per gate
+  read that coefficient at every gate visit
   enumerate every window and span case
   check all formal columns and rejection controls

Claim type: scoped exact implementation improvement with finite differential evidence and a local performance measurement. No new mathematical obstruction, supplier admission, kappa or selected-frontier change is claimed. Eight files are added under research/p440-decoded-pulse-replay; the frozen predecessor and shared code are unchanged.

This contribution was produced by Nick Petalas. Credit Hanson Sun / bbMisk for PR1431, its theorem, interpreter, complete independent caller and receipts; Marius-Paul Dumitrean / PR1337, Rohan Arun / PR1297, Jeremy Kothe / PR1274 and the retained construction lineage keep their credit. Advance CLAIM.

Evidence

• Before: five complete baseline processes took a median 5.885767 s, range 5.675676 to 5.941731 s. After: five alternating prepared processes took a median 4.949344 s, range 4.796746 to 5.208318 s. All ten succeeded with identical output hashes and zero errors. Preparation and source loading are inside the timed processes. BENCHMARK.json is the generated receipt bound to implementation, harness and source-manifest hashes.
• The complete caller retains 2,757 nonzero windows, one zero window, 1,611 directions, 5,177,758 classified span cases, the 704-column dirty-input identity and all three source rejection controls. Its full window/direction hashes and saved complete-result equality remain active.
• New checks cover 2,706 exact pulse-recurrence comparisons and five source/boundary rejection controls. Warning-strict normal and optimized direct runs pass in 10.631 s and 10.481 s. Both registered commands pass through research_package.py in 21.298 s total, below their individual 180-second limits. The package verifier emits PASS_P440_PREPARED_REPLAY; the runner emits PASS_REGISTERED_RESEARCH_PACKAGE.
• Committed-byte/source-history preflight passes at a216bf8e5d4326d2fd313278a910d46ce76b8133, covering all eight package files and four live inputs. In-memory syntax, JSON, function-length and staged-whitespace checks pass. Worktree status including ignored files is clean.
• Environment: CPython 3.12.15, macOS 27.0.1 arm64, 18 logical CPUs. Pre-run load averages were 2.61, 2.50 and 1.92; other research can run concurrently. The profile identifies donor-pulse execution as the dominant cost. Timing ranges do not overlap, but the speed claim remains local to this workload and machine.

From the repository root, using the CPython 3.12 standard library:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/p440-decoded-pulse-replay/fast.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/p440-decoded-pulse-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/p440-decoded-pulse-replay/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/p440-decoded-pulse-replay
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/p440-decoded-pulse-replay --check-source-history
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/p440-decoded-pulse-replay/benchmark.py

Another CPython 3.12 installation can replace the absolute interpreter path. Add --baseline to fast.py for the original interpreter. The benchmark is opt-in and prints its receipt; redirect outputs outside the checkout.

Limitations and unrun obligations

The measured surface is the complete independent PR1431 caller. The primary verifier, predecessor test-suite timing, other pivots, shared-tool integration and selected supplier cold replay are outside the claim. The adapter is opt-in and source-bound. It preserves existing mathematical checks and does not independently audit the predecessor theorem as its deliverable.

No native, compiler, ownership, precision/tape or analytic-recovery assumption is discharged. No complete multiplication theorem follows. Lean, Docker and a separate static analyzer were not run. All registered local commands ran; no local correctness obligation is deferred to CI. Independent human and formal proof-kernel review are unclaimed.

Open next questions

• Can exact sparse-state zero handling reduce the remaining pulse cost? Start with the prepared complete profile and cancellation, scale-zero, dirty-state and pulse-boundary tests. No such shortcut is supplied here.
• Should a maintained successor adopt this execution? Start with one explicit caller and preserve all four pinned inputs and full saved-receipt checks. Source integration and broader timing remain open.

Related open work

The completion refresh listed this account's sixteen open PRs created since the advance CLAIM at 2026-10-30T13:51:14Z, including this PR. None of the fifteen other contributions studies the PR1431 pivot-440 independent caller or computes its window/span quantities or timing. No same-instance numerical disagreement was found, and no extra computations checked another submission. The merged PR1431 is the direct predecessor.

Adjacent replay-engineering work uses different callers:

• PR6270 changes the bounded rational parameter optimizer's complete solve/check path, with a different fixture and receipt.
• PR6272 changes exact rational-rank certificate products, rather than fixed-gate pulse propagation.
• PR6274 changes the PR4841 mapped-contact distance caller using binary basis ranks.
• PR6279 caches path prefixes in PR5235's dirty-circuit certificate caller, with a separate cache contract and complete workload.
• PR6281 substitutes exact Gaussian-dyadic matrix products in PR5210's nonlinear support caller.
• PR6282 uses intersection counters in PR5729's complete E7 classification caller.
• PR6283 skips exact-zero row updates in PR5785's sparse coupled-recurrence CLI.

No performance comparison is asserted across these different source objects. This bounded overlap refresh does not exclude unpublished work.

CI notes

Both hosted checks passed at exact contribution head a216bf8e5d4326d2fd313278a910d46ce76b8133 in run 41067724331: plan in 4m14s and replay (research/p440-decoded-pulse-replay) in 2m35s. The completed check list was read once. Separate run metadata confirms the matching head, completed status and successful conclusion.

Every registered command and committed-byte/source-history preflight also passed locally. Hosted replay certifies execution of the registered normal and optimized finite checks and source bindings. The timing measurement remains local; CI has no machine-dependent performance threshold. Independent human and formal proof-kernel acceptance are unclaimed.

Merge Danger

Door: two-way.

Blast Radius: isolated.

One opt-in package is added. Its implementation loads authenticated predecessor bytes into a private module. Frozen sources, shared code and selected metadata are unchanged.