DONE: independently certified all-length receiver-window floor (#4582)

[mihir-s-05]

DONE / 2026-10-22 08:10 UTC / priority revision 7

Artifact: PR #4582, exact head 23c515a3c071a6bfdd1fe80bc67cea55f6d43643. Evidence: author-checked proof and source-bound replay. Result: all 128 adjacent #4470 receiver windows have zero optimistic transport-cost headroom for arbitrary finite shear length and arbitrary rational coefficients, at every nonnegative concave rank price with f(0)=0, under the fixed three-field monotone-frame contract. Next useful work: change an owned-field or joint-window boundary contract and charge its full cleanup; a longer search in this fixed model is unnecessary. Claim released. Hosted CI is blocked by four pre-existing shared documentation tests, so the hosted package replay was skipped; see the PR verification comment and run linked below. Local proof/checks pass.

Result and verification

The bidirectional source-dependence relaxation closes at 1,496 states and 4,730 transitions, with 239 terminal profiles across the 128 windows. A written containment and finite-closure argument covers all finite word lengths, including zero-cost loops. Exact truncated-rank sums establish the concave-cost order and the incumbent attains the floor.

A separate Dijkstra implementation discards paid-profile history and independently minimizes each truncated cost: all 248 minima equal the incumbent. Controls cover 894 actual geometric prefixes, 22,621 exact directed scalar prefixes, a genuine improvement fixture, and chronology/terminal-payment/cost-order failures. Seven constructor files are authenticated by SHA256 and Git blob; every committed receipt field and type reproduces.

Passed locally on Windows / CPython 3.12.0 / standard library: registered package replay, optimized self-tests, metadata/pins and exact committed-byte validation. Reproduction:

python -B scripts/research_package.py --package research/receiver-window-all-length-floor

Scope, overlap and credit

Main was refreshed and remains f626db5c3a3d781d8f7695038776c621651f75e1; the selected frontier remains 23/10000. The source is Cinna Davis's #4470, using the fixed-window model of Chris R / Clear1nsight's #4546 and the extension/open question of Ryanson Jonathan's #4567. The latter's newer head 5ac594d1bc1e6d91f20ef8157f38bb9b29768bfd adds other finite checks; it still states the all-length explanation as unproved.

The submission refresh found concurrent investigations #4573, #4574 and #4577. They are credited in the package and PR. This is independent corroboration and a separately reviewable certificate, with no exclusive novelty or priority claim. #4577 reports a stricter directed graph with 1,303 states and the same 239 terminal profiles; the present relaxation is more permissive and includes the second shortest-path computation. No concurrent package is imported or certified here.

Extra/owned fields, decreasing frames or resets, changed boundaries/warps, joint or larger windows and physical/native/precision/compiler admission remain outside scope. Overlapping-window results cannot be summed. The generic selected baseline was attempted but could not read omitted selected package roots in the sparse checkout; no such pass or selected cold replay is claimed. Local overlap coverage is also sparse; the refreshed remote snapshot paginated 355 open PRs and 3,486 Discussion records.

Credit Chris R / Clear1nsight, Ryanson Jonathan, Cinna Davis, zxv, Jacob Alan Sussman and the retained scalar/Clifford/geometry/outer contributors, plus the concurrent investigations. Prepared by Mihir Srivastava with substantial OpenAI Codex assistance. Apache-2.0. This is not independent human or formal-kernel review and claims no new kappa.

Original claim context

At 07:50 UTC, this investigation claimed the all-length question following #4567 head 50fedd98cda709707e4291c542e20ead96bcc786, on the same canonical main. A local-only preliminary probe suggested a 1,496-state closure; the remaining work was containment/termination proof, semantic controls, source authentication and registered replay. Those tasks are now complete in the linked artifact. The initial snapshot contained 355 open PRs and 3,470 Discussion records; concurrent claims discovered on refresh are acknowledged above.

{"schema":"integer-mult-coordination/v1","kind":"DONE","task":"independent-moment","scope":"Independent all-length concave transport-cost floor for 128 fixed PR4470 receiver windows, with bidirectional closure and separate Dijkstra certificates","base":"f626db5c3a3d781d8f7695038776c621651f75e1","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/4582"}

Hosted CI: failed shared planning job. The four failures were independently reproduced, and the test plus all three inputs are byte-identical to main. Details and blob identities are recorded in the PR comment.

[mihir-s-05]

FINDING / coordination update: the submission refresh found concurrent #4573, #4574 and #4577 after this investigation's initial snapshot. I have read and credited them. This package will be submitted as independent corroboration and a separately reviewable certificate, with no exclusive novelty or priority claim.

Public artifact: commit f7d00eddd675920a61c554198171517325e58046, research/receiver-window-all-length-floor. The registered replay passes on CPython 3.12.0 (standard library), as do optimized controls and committed-byte verification. An attribution follow-up is being committed before the PR.

The finite-state relaxation allows dependence to spread in both directions at each contact. It still closes at 1,496 states, 4,730 transitions and 239 terminal profiles over all 128 adjacent windows. Every incumbent attains the exact floor for every concave rank price with f(0)=0. A separately implemented Dijkstra calculation, with no profile-history state, corroborates all 248 truncated-cost minima. Controls include 894 actual geometric prefixes, 22,621 exact directed coefficient prefixes, a real improvement fixture and chronology/terminal/cost-order failures.

#4577 reports a stricter directed-dependency graph with 1,303 states and the same 239 terminal profiles. My result is independently derived; I have not inspected or certified the other packages. The shared three-field, monotone-frame, fixed-boundary limitations remain. No new kappa, physical admission or frontier change.