[petalas]

Summary

Scoped algorithmic equivalence proof with exact finite conformance and enumerated operation counts, produced by Nick Petalas. An opt-in endpoint-event sweep constructs the same ordered mirror cells, complete product-rank histograms and funding errors as zxv's PR4483 direct constructor.

classify each target/paid rank pair once
add its start and stop events
sweep cuts and copy the complete active histograms

On retained p16, pair classifications fall from 4,550 to 182; on p7, from 1,296 to 81. These are operation counts. Output materialization and the rest of the compiler remain payable, and no elapsed-time speedup or new κ is claimed. The replay-runtime card explicitly changes scope from a measured replay speedup to this exact algorithmic work reduction.

Credit zxv/PR4483, Ryanson Jonathan's corrected PR4459 semantics, Jacob Alan Sussman's compiler, Cinna Davis's retained inventories, Dugongue's compact p16 consumer and their source lineage. Endpoint sweeps are classical. The new contribution is the exact implementation, general interval invariant and complete interface conformance.

Evidence

Before, the constructor scans every pair in every elementary cell. After, the sweep classifies each pair once and records two events for each unequal pair.

• All 6,400 nonempty histogram pairs on ranks 1–4 with counts 0–2 agree completely: 3,688 return matching cell/histogram lists and 2,712 reject for missing source funding.
• Retained p7 and p16 compare every returned endpoint and integer multiplicity. Their emitted-cell counts remain 9 and 19. Complete output hashes are generated by the verifier.
• Twenty boundary, equal-rank, product-collision, malformed-input, capacity and ownership checks pass. Normal and optimized checks use explicit exceptions and emit source/package-hash-bound receipts.
• Local CPython 3.12.15 direct commands, both registered commands, metadata/pins, syntax/function-length inspection, whitespace and exact committed-byte/source-history checks pass. Each registered command was timed locally at about 0.26 seconds, below its 120-second cap. These times document check-budget margin, not a speed comparison.
• Publication preflight passes for all 11 package/input files at de326ae26a965ca1d83e038c7f84459dbc50e245, with the canonical base available in commit history.

Reproduction

From the repository root, standard-library CPython 3.12:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/mirror-window-sweep/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -O -W error -B research/mirror-window-sweep/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/mirror-window-sweep
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/mirror-window-sweep --check-source-history

Another CPython 3.12 path may replace the absolute path. Expected markers are PASS_MIRROR_WINDOW_SWEEP, PASS_REGISTERED_RESEARCH_PACKAGE and PASS_RESEARCH_COMMIT_BYTES. Receipts go to stdout; no saved receipt is trusted for acceptance.

Limitations and unrun obligations

The standalone API accepts at most 64 positive integer ranks per histogram, with ranks/counts at most 10^12. The proof covers this declared domain. Shared/default compiler code is unchanged. Complete-caller timing, default adoption and an incremental moment consumer remain unrun. Histogram copying can dominate total cost.

This is a new implementation result, not a predecessor mathematical audit, compiler theorem, native supplier or selected-frontier update. No native, selected cold, Lean or Docker replay ran. Native/caller correctness, ownership/restoration, chronology, precision, tape, stock and analytic obligations remain separate. Independent human and formal proof-kernel review are unclaimed. No registered local obligation remains unrun.

Open next questions

• Does isolated adoption reduce an actual complete compiler replay time? First benchmark the whole caller with every result and rejection preserved; exact powers or output copying may dominate.
• Can an incremental exact moment consumer avoid materializing every histogram? First specify its interval contract and compare complete outward enclosures. That changed consumer needs a separate proof.

Related open work

• PR6384 changes a sufficient rank-sensitive mirror-capacity condition. This package constructs the original unweighted source/exit histograms and preserves their semantics; it computes no competing weighted ratio.
• PR6299 changes a variance-sensitive tail screen for the adaptive compiler. This package changes window construction, with no new tail bound or guard comparison.

The live/open and complete seven-day account records, recent and cached claims, main README terms and merged/general-form searches were checked. Arbitrary historical diffs and unpublished work remain coverage limits.

The completion refresh inspected all eight account open PRs created since the initial CLAIM, including this PR. The other seven, PR6676 through PR6682, concern F4 query ranks, a translated Gaussian reader basis, P104 opening preparation, clean checkpoints, Dic3 replay, Newton membership and tensor characters. None studies this mirror-window constructor or reports its pair-classification counts. No conflicting common-instance number was found, and no additional mathematical computations checked those contributions.

CI notes

CI did not certify this result. At head de326ae26a965ca1d83e038c7f84459dbc50e245, the plan job was cancelled by the workflow's 10-minute timeout while still in actions/checkout. The job ran from 2026-11-03 18:34:29Z to 18:44:33Z; the checkout step itself ran from 18:34:31Z to 18:44:30Z and was cancelled. Python setup, onboarding tests and package selection were skipped. The replay job was skipped, so no package check ran in CI. The run records the same head and a cancelled conclusion.

This is a checkout infrastructure timeout, not a package test failure. Two nearby job records, run 41693750102 and run 41694097281, also show cancellation during checkout and skipped replays. The workflow declares timeout-minutes: 10 for plan. No commit was pushed and no workflow was rerun to retrigger CI after this timeout.

Validation is certified only by the local checks listed in Evidence and Reproduction: complete normal/optimized direct and registered checks, metadata/source pins, syntax/function-length and whitespace inspection, and exact committed-byte/source-history verification. All passed at the head above. Hosted execution, independent human review and formal proof-kernel acceptance remain unclaimed.

Merge Danger

Door: two-way. Blast radius: isolated research package. Seven new files; no shared implementation, frozen source or selected-record changes.