DONE: complete direct584 commuting cover survives all existing-boundary relaxations

[RossRichardson]

DONE / FINDING — complete direct 584 four-read commuting-retiming obstruction.

Artifact: PR3594, publication head e3dc9c1660bfec0501dd7522f44a21746f9b89e2; proof and standalone replay.

Deleting entering helper 584 through direct carrier 439 delivery preserves the complete arbitrary-dirty operator, but every allowed adjacent-commutation placement of the four reads to 168,150,56,115 fails the common-frame/monotone-contact contract. The complete cover has 1,002 contact classes per provider. Every one of the 2,004 final certificates runs from an original input port to a target output with no interior native boundary. Consequently arbitrary native chart/phase changes at all existing slots and arbitrary helper entrance/terminal-frame changes cannot repair this fixed scalar family. This does not exclude changed scalar consumers, added/moved native slots, or changed input/output contracts.

The verifier derives the 6,144 slot/order choices and exact 1,002-class feasible cover, reconstructs actual words, and checks every consecutive physical touch. It imports no optimization graph or predecessor auditor. Complete rational free-operator forward/dual checks cover the original-cut and both extreme representatives on 631 independent inputs and 90 private buffers; a written commutation argument covers the rest. Twenty defect controls reject incorrect signs, stale cleanup, noncommuting-boundary crossings and invalid or reset-skipping path claims. Registered replay passed in 154.49s and optimized Git-free replay of the committed export in 170.76s; exact publication bytes, source-history availability and final export integrity also pass. Separate AI review checks the coverage by elementary-matrix commutation and interval-order feasibility. That review script is local; independent human review is not claimed. Hosted CI is separate and is not yet claimed passed.

Base canonical main: 20ecf2891d80b5acf18d980b2164fb44ea7faa90, refreshed 07:11UTC, priority revision 6. Source: dcharb78's PR3133 head 51eb9c4ee9e4722010d308aa3309e039d3940cc2, with Marius-Paul Dumitrean/PR2979, Jeremy Kothe/PR3015, PR3042 and the source's full credited lineage retained. Existing fixed-word frame and normal45 A-retiming work has a different domain. Submission overlap covered 308 open PRs and 2,430 Discussion records with complete reported pagination and no warnings; no exact four-read cover was located, which is not a proof of novelty.

Open next question: change one scalar consumer contact or introduce/move one native slot, then derive a valid path or exact realization on one rejected class before a broader search. A survivor must retain arbitrary-dirty cleanup and native phases and pay the complete local/idle/owner/precision/outer invoice. Existing native/helper boundary changes alone are closed here. No supplier, larger conditional κ, selected-frontier change, all-size barrier or formal-kernel proof is claimed. This scoped contribution is finished; no active claim is retained.

Prepared by Ross Richardson with substantial OpenAI Codex assistance.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "independent-moment",
  "scope": "Complete direct584 four-read commuting cover with all existing native/helper boundaries relaxed",
  "base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
  "expiry": null,
  "artifact": "https://github.com/CrocSwap/integer-mult-bounds/pull/3594"
}