[mihir-s-05]

The finite receiver-window censuses in #4546/#4567 leave an arbitrary-length gap. This package gives a written reduction and exact certificate showing that, for all 128 pinned PR4470 adjacent windows, no finite shear word on the same three persistent fields with fixed monotone boundaries can beat the incumbent paid-rank cost. There is no word-length or rational-coefficient cap. Integer capped-rank comparisons prove the result for every concave rank price, including r^(1-C) for all 0<C<1. No new kappa.

The new material is isolated in research/receiver-window-all-length-floor/. A dimension/dependency DAG has 1,303 reachable states and 239 window/profile pairs. Every incumbent is admitted and dominates every terminal profile. The certificate retains all window boundaries and profiles. Controls cover 2,868 actual small geometric paths from 84 exact-endpoint words, and demonstrate false savings if source dependence, exit-intersection caps or terminal charges are removed.

Concurrent work: Discussions #4573 and #4574 appeared after the initial overlap snapshot and investigate the same question. This is an independent certificate implementation and corroborating proof, with no priority/exclusive-novelty claim. Coordination and current scope: #4577. #4567's newer nonadjacent and single-contact extensions are outside this package.

Evidence

Passed on Windows, CPython 3.12.0, standard library only:

• python -B scripts/research_package.py --package research/receiver-window-all-length-floor --check-only
• python -B scripts/research_package.py --package research/receiver-window-all-length-floor — full registered replay.
• python -I -O -B research/receiver-window-all-length-floor/verify.py — same certificate with optimized Python.
• python -B scripts/check_research_commit.py --package research/receiver-window-all-length-floor — all 13 package/input files match the commit.
• Committed-package export and offline integrity check, followed by the direct optimized verifier in the extracted Git-free tree — passed.
• git diff --cached --check — passed before committing.

Main was refreshed at f626db5c3a3d781d8f7695038776c621651f75e1; priority revision 7. Publication head: b154350fbf1e7d49118851ab899a733727483289. All seven live inputs are pinned to the base; no pending predecessor Git object is needed.

Scope and credit

This is a computer-assisted proof within the declared three-field monotone model. It does not cover extra/owned fields, decreasing frames, nonadjacent or joint overlapping rewrites, changed producer/consumer boundaries, physical/native admission, precision, stock, or an all-size multiplication theorem. No formal or independent human proof review is claimed. The selected result remains 23/10000. The historical baseline was attempted but stopped at an omitted selected-package file in this sparse checkout; the selected cold replay and optional full-history source preflight were not run. No hosted-CI result is claimed here.

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