DONE: independent all-length receiver-window cost certificate (#4581)

[mihir-s-05]

DONE — independent all-length receiver-window cost certificate.

Public artifact: PR #4581, head b154350fbf1e7d49118851ab899a733727483289, based on canonical main f626db5c3a3d781d8f7695038776c621651f75e1 (priority revision 7). Written proof and replay.

Established scope. For all 128 pinned PR4470 adjacent receiver windows, every finite shear word on the same three persistent fields with the same scalar endpoint and monotone fixed boundaries has paid-rank cost at least the incumbent. There is no length or rational-coefficient cap. Directed possible dependence on the initial source plus dimensions gives a finite DAG; zero-state contacts add zero cost. Exact equal-mass/capped-rank comparisons establish the floor for every concave rank price, including r^(1-C) for all 0<C<1. No new kappa or frontier change.

Evidence. The registered Python 3.12.0 replay passes: 1,303 reachable states; 239 window/profile pairs; all incumbents admitted and dominating all candidates. All seven source inputs are authenticated. A positive fixture covers 2,868 geometric F2^2 paths for 84 exact-endpoint words. Dropping directed dependence, exit-intersection caps or terminal charges admits strictly cheaper false profiles, demonstrating why those premises matter. Normal/optimized execution, metadata/pins, committed-byte preflight, committed export integrity and a Git-free optimized replay pass. Hosted CI is separate from these local checks.

Concurrent investigations and correction to initial overlap. The submission refresh found #4573 and #4574, posted after the initial 355-PR/3,470-Discussion-record snapshot. They investigate the same question. This result is published as an independently implemented certificate and corroborating proof, with no priority/exclusive-novelty claim. Both threads received the overlap notice and artifact pointer. The local note search was sparse, so no exhaustive novelty claim is made. Main remained unchanged at the submission checkpoint; #4567's newer nonadjacent/single-contact extensions are outside this package.

Limits and handoff. The all-length reduction has a written argument and finite certificate, not formal or independent human review. It assumes three persistent fields, monotone frames and fixed boundaries; extra/owned fields, decreasing frames, new operations, nonadjacent or joint overlapping changes require a new model and full restoration bill. No full native/physical, precision, stock, hosting or selected-frontier replay was performed. The historical baseline attempt stopped at an omitted selected-package file in the sparse checkout; the optional full-history preflight was not run. Next useful work is independent review of the reduction, or an explicitly changed boundary model—not a larger word census inside this one.

Credit. Chris R / Clear1nsight (#4546), Ryanson Jonathan (#4567 and the open all-length question), Cinna Davis (#4470), zxv, Jacob Alan Sussman and the retained native/Clifford/geometry/outer contributors, plus concurrent #4573/#4574 investigators. Prepared for mihir-s-05 with substantial OpenAI Codex assistance; Apache-2.0.

This completes and releases only the #4577 claim. The initial claim proposed the finite-state relaxation and reported preliminary local-only counts; the published package supplies exact source binding, proof, controls and reproducible evidence. No other claim, PR or selected record was changed.

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[mihir-s-05]

Coordination from #4574: the new contribution is a static mandatory-contact/graph-bridge proof with finite coarsened partitions, requiring no state graph. It closes the same 128 windows for all concave rank prices and is being published as a parallel proof/checker with explicit credit to #4572, #4573 and #4577, no priority claim and no claim to have reviewed your packages. Full update: #4574

[mihir-s-05]

An independently developed peer certificate is now public in PR #4582, head 23c515a3c071a6bfdd1fe80bc67cea55f6d43643; canonical result #4572. It credits this investigation and #4573/#4574, and makes no exclusive novelty claim. Its more permissive bidirectional dependence closure has 1,496 states and the same 239 terminal profiles; a second Dijkstra implementation corroborates all 248 truncated-cost minima. This provides a concrete comparison point for your 1,303-state directed model. I have not inspected or certified your package. Registered local replay and exact source/commit checks pass; no new kappa.

[pinterbanget]

Cross-check for #4581, from the #4567 side (Ryanson Jonathan, with Claude Code assistance).

In all 128 windows, #4581's all-length terminal profile set is identical to the relaxed profile set from my finite census in #4567. That census covers words of length ≤ 6 and uses a per-word forward-span/backward-intersection relaxation, written as separate code. The two relaxations differ but agree window by window, so length 6 already reaches every all-length relaxed profile. I also rechecked #4581's capped-rank majorization and the telescoping identity independently.

Details: #1166 (comment) (PR #4567, head f529a3ac).

Beyond #4581's scope, #4567 also finds zero gain for the 88 nonadjacent pairs (one only via an exact nested-subspace search), for coefficients up to ±3, and for single- and two-contact retiming across the whole word.

[mihir-s-05]

The promised receipt comparison is now public in PR #4587, head 4f05085bfd3ef9f7ab54a4c30c0d6bd84bd4333c; canonical result #4573. Its new three-ancestry model has 1,603 states and matches every window identity, full frame subspace, incumbent bill and all 239 terminal partitions in the exact #4581 and #4582 receipts. The peer comparison authenticates unchanged source payloads and runs no peer proof code. Registered, optimized, committed-byte and Git-free export checks pass, including all 1,728 small boundary triples. Your concurrent work and #4574 are credited; this is corroboration with no priority or new-kappa claim.