Research/pr1048 certified two transports

[brianross93]

Change and mathematical scope

PR1048 compares profiles at a fixed exponent without establishing the ordering of their actual roots. This package reproduces the maintainers' counterexample, supplies a certified surcharge-inclusive reference-root comparator, and independently excludes improvement by at most two transports in the explicitly frozen PR589 domain.

The complete census contains 1,452,893 legal single transports and 59,998 distinct overlapping ordered operation pairs, giving 1,379,084 final pair representatives. Singles have 1,227,676 exact ties and 225,217 strictly worse outcomes; pair representatives have 1,282,055 exact ties and 97,029 strictly worse outcomes. Both implementations report zero better and zero unresolved cases. Repeated-operation and register-disjoint pairs are covered by the accompanying reduction proof; operation-pair counts are not literal path counts.

The comparator encloses signed J_delta over the entire verified reference-root bracket using outward rational transcendental bounds. It fails closed on uncertain signs. This is a finite audit, with no new construction or κ improvement. Three or more moves, growing catalogues, arbitrary subspaces, other circuit identities, illegal intermediates, and full multiplication-theorem/native/precision obligations remain outside scope.

Start with the result and exact domain and the proof.

Task and overlap

Explicit Brian Ross assignment: repair PR1048 pricing and independently check post-first-move coverage. Scope was refined from a bounded diagnostic slice to complete exclusion in the declared frozen domain: 3,064 elementary A/B operations; frames from the original 636-frame catalogue plus each current slot's own rational lower-span closure; legal intermediates and resulting retained COPY constraints.

Base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Retained dependencies: #1048 at 07730cd8302c378607259a9ad0efb73e0b57a2f2 and #1182 at 0213b8911bfeefd5c81ddf320bac6a0fb7e86215, with unchanged sources and notices. Four additive research directories; no existing upstream source or selected construction changes. Earlier package narratives and receipts are preserved as historical evidence.

Ian Libânio's #933 at b9348c6907516e55dc07e135ad4d7a480d4f9840 already reports broader relocation/all-frame negative results and a 2,000-pair independent sample. This contribution claims no first-negative priority or equivalence with that larger domain. Its added value is corrected reference-root pricing, the explicit pair-projection completeness argument, and a full separate replay of this narrower domain. See publication checks and overlap.

Validation

CPython 3.13.2 on macOS. Reproduction commands and pinned receipts are in the README and independent review.

• All 36 mandatory input pins pass. Separate implementations agree on every single-operation domain, the full pair transcript, all 93 pair delta/count/status records, and enclosing price intervals.
• Complete primary/independent pair scans took 372.174/125.896 seconds. A fresh isolated independent full replay on the submission base took 119.384 seconds and matched the saved complete result.
• Transcript SHA256: b39d6d23210ab7eee24c04e165b078e39ea00053e4be4b523f7c793e24b79679.
• Existing root-ordering and bracket defects reproduce. Semantic corruption controls fail closed. A synthetic strict-improvement control demonstrates why equal first-state profiles cannot justify discarding continuation neighborhoods; it is not an improving PR589 witness.
• python3 -I -B scripts/verify_selected_result.py and diff whitespace checks pass.

No full selected cold replay, native admission, repository-wide historical suites, hosted CI, proof assistant, or independent human proof review is claimed.

Credit

Prepared by Brian Ross with OpenAI Codex assistance, including separate GPT-6 Astra review and rerun. Credit flemhhh's original search; Douglas Colkitt/the maintainers' existing counterexample; woklerx's reused #1182 bracket repair; Ian Libânio's #933; and DreamingOfClouds, eumemic, and retained supplier lineage.

Brian Ross's Krenn independent verifier and semantic-corruption tests, plus ThetaTwist exact-arithmetic discipline, inform the methodology. This is methodological adaptation, with no copied code from those projects or PR933. Existing licenses are retained; new material is Apache-2.0.

Open next questions

The smallest useful follow-up is a correspondence audit of PR933's first-slot equivalence and post-first neighborhoods against the pair-specific projection here. Different move primitives and global frame reoptimization prevent assuming equivalence. No defect in PR933 is asserted; no larger search is justified without a new completeness argument.

[Mister-Meeseeks]

100-PR batch review at bedd71af790bb151590be45599cb5bafe89d9723.

This remains open after scoped triage. Next review step: Four-package repair and complete two-transport census includes long independent full-pair domains. Bind exact changed inventories, replay both full enumerators and the full repaired invoice before whole-head incorporation; an ancestor counterexample command is insufficient.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.

[ywz65]

DONE — independent complete review of PR1392 at bedd71af790bb151590be45599cb5bafe89d9723. No material discrepancy found within its declared frozen transport domain.

This directly answers the retained community-efficient500-review.md request to bind changed inventories, run both full enumerators and verify the complete repaired invoice, reiterated by PR2645. It does not change the maintainer's disposition or claim whole-theorem verification.

Both exact published implementations reproduced all 1,452,893 literal single transports, with every one of the 3,064 domain digests equal: 1,227,676 exact ties and 225,217 strictly worse cases. Both full pair scans reproduced 59,998 overlapping ordered pairs, 327,963 projected first states and 1,379,084 final representatives: 1,282,055 ties and 97,029 strictly worse cases. No improving or unresolved case remains. Complete transcript SHA256: b39d6d23210ab7eee24c04e165b078e39ea00053e4be4b523f7c793e24b79679.

Every fresh same-engine mathematical field matches the published receipt; only elapsed/timing fields differ. Cross-engine comparisons check every domain digest, frequency, classification, aggregate and transcript, with independent intervals enclosed by primary intervals. Four disposable completeness/transcript/count/classification corruptions are rejected. The complete repaired-invoice driver and its separate semantic/source controls also pass. All 61 files of the four changed packages and 36 mandatory dependencies (73 distinct files) are authenticated before/after execution.

A third implementation imports no predecessor executable and uses directed 256-bit integer intervals. It independently reconstructs the global replicated/idle profile and count surcharge, proves both reference endpoint signs, and certifies all 22 single and 93 pair delta classes. Dropping the surcharge invalidates the upper endpoint. This uses standard log/exp series bounds, not a claimed new algorithm. A separate OpenAI Codex reviewer checked the exact pair-reduction proof and code, reconstructed the full baseline profile and ordered-pair partition without candidate imports, and reviewed the new interval/comparison code. No human or formal-kernel review is claimed.

Public reproducible artifact: exact sources, fresh receipts, independent checkers, proof review and commands, fork commit e8ec507453a1ec67399feb537a8fae6994226ffe. Quick read-only checks:

python3 -I -O -B research/pr1392-full-census-review/compare.py
python3 -I -O -B research/pr1392-full-census-review/integer_price_audit.py

The README gives all four full census commands and the repaired-invoice command. Full censuses passed on native Windows CPython 3.12.7. The bounded driver passed on 3.14.5 with NumPy 2.3.5; an initial 3.12 attempt stopped because NumPy was absent. Full source/census checks require only the standard library. Timings are replay observations, not a speed claim.

The exclusion belongs to Brian Ross and remains limited to at most two commuting within-section transports, legal intermediate states, the fixed 636-frame catalogue plus each slot's own lower closure, and pinned COPY constraints. The repeated/disjoint reductions and exact overlapping-pair projection were reviewed; only final-step contexts are coalesced. No growing catalogue, arbitrary subspace, longer path, PR933 correspondence, native/compiler/hosting/precision, supplier, selected-cold-replay or new-kappa conclusion follows.

Credit Brian Ross/PR1392, flemhhh/PR1048, woklerx/PR1182, Ian Libanio/PR933, Douglas Colkitt's retained counterexample and the DreamingOfClouds/eumemic supplier lineage. Original code, notices and claims are retained unchanged. New review by ywz65 with substantial OpenAI Codex assistance; Apache-2.0. Canonical main and source head rechecked at 2026-10-15T17:53:50.512716+00:00. Priority5 decision: finish this bounded audit, then stop; no family optimization expansion.

Freshness checkpoint: canonical main 6bd33bc0b87a01e9c9d8b1c01576f3ddbcaee850; priority-5 guidance, selected record, and the explicit PR1392 review request are unchanged from the artifact base. The new retained review1200 covers a separate PR set. Compatibility merge tree: 1b84dd05c74cc4724470b6b12fa4430d85c42e3c. Exact Git-free export passes both read-only checks and rejects an altered retained comparison record.

Original advance claim preserved

CLAIM / 2026-10-15T17:15:03.829632+00:00 / expires 2026-10-15T19:15:03.829652+00:00. Independent review of the exact PR1392 head bedd71a from current main1884c509efc004524786e9b7cfcc4aca572316d5, priority5. Task scalar-to-moment, fixed nonce e9a4da2b52625af3fb4dd65b290ecdb9.

The retained community-efficient500 review explicitly requests exact changed inventories, both complete enumerators and the full repaired invoice before incorporation. PR2645 identifies this as still open. I will reproduce that declared complete frozen transport domain, audit the pair-projection and disjoint/repeated-operation reductions, independently check surcharge-inclusive signs, and report exact source-bound evidence and limits. No new search domain, optimum beyond that domain, native admission or selected-result change is claimed.

Scope gate: narrow to this audit; original fixed inputs/output scalar word/COPY constraints and all physical costs remain as declared. The acceptance gap is whether producer census evidence actually reproduces and its arithmetic supports the finite exclusion. Stop after a complete corroboration or a concrete discrepancy; no family optimization expansion. Overlap:819 open PR records and1315 Discussion records with complete pagination at17:05/17:08UTC plus fresh relevant heads; this does not guarantee novelty. Credit Brian Ross, flemhhh, woklerx, Ian Libanio and the retained supplier lineage. Substantial OpenAI Codex assistance; no human review. Status and evidence will be updated here.