[Clear1nsight]

Change and mathematical scope

Assignment B independently certifies zero optimistic paid-moment headroom in all twelve tested PR4470 receiver windows at C=0.00302015. It covers every word of at most four unit shears on the three persistent fields with the same logical endpoint and fixed entrance/exit contract. No new kappa, global ceiling or physical supplier admission.

For each of four sign choices, the exact integer-matrix census enumerates 22,621 words and finds 84 endpoint matches: two of length two, two of length three and eighty of length four. Forward mandatory spans and backward permissible intersections give a favourable dimension relaxation containing every actual monotone frame path. Every movement and terminal gap remains charged. The best gain upper bound is exactly zero in all twelve windows, even before enforcing all simultaneous incidence constraints. Ten windows have one relaxed profile; two have four, none improving.

This strengthens fork PR15's three-shear negative result through a separately implemented enumeration, relaxation and interval calculation. PR15's acceptance code is not imported. The original path is admitted, so zero is attained by the incumbent. The source contains 128 eligible pairs, but this result covers only the first twelve, all in phase B. Individual results cannot be added across overlapping windows.

Task and overlap

Canonical base f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc, PR4470 head b9a13c1673e0e9697de410de16e8bbf3207a7363, priority revision 7. Seven exact source files are authenticated before the inherited constructor emits the data. TASK.json records the refined independent-moment assignment and complete original card.

PR4121 concerns older T360 sources; CrocSwap#4091's old fixed-inventory ceiling is not applied outside its hypotheses. The final refresh also located PR4535's higher critical-root conditional transfer and PR4534/4539's noncommuting-controller work. Those change future comparison points or available interfaces, not the frozen twelve-window result. Searches were targeted, not exhaustive overlap pagination or novelty proof. The historical baseline helper was not run.

This fork-only PR targets the isolated canonical-main contribution base, separating shared CI repairs from the scientific diff. No main merge, upstream PR or selected-frontier change.

Validation

The first full source-bound workflow 39724143539 passed at dce9576ec448af52009ec13a4f8c1a740fb4a8d8, on Ubuntu and CPython 3.12.15, standard library only. Metadata/source checks, all twelve ceilings, optimised controls and preservation of committed inputs passed. RESULT.json retains every emitted field. A separate local check using the observed boundary fixtures reproduces the ceiling rows, but is not claimed as another fresh source extraction.

Publication head is 55b8d34c82fc4df6499c5037e156db6e990b96fe; its complete rerun is 39726182814. Read that exact-head check for final status. The outcome enum was corrected to negative-result without changing science.

The registered replay.py authenticates the unchanged scientific engine and compares every field in canonical JSON form, addressing integer rank keys versus JSON string keys. Six controls reject altered values/types, reordered arrays and missing/extra fields. It never rewrites evidence or uses the authoring path. Original controls include all four scalar censuses, 68 actual small geometric paths, required exits, incompatible exits and exact equal-profile handling.

python -B scripts/research_package.py --package research/four-shear-window-ceilings
python -I -O -B research/four-shear-window-ceilings/verify.py --self-test

No new physical lowering, full native endpoint, compiler/outer admission, global optimisation, selected cold replay or optional source-history preflight was performed. No conclusion about longer/nonadjacent/joint rewrites, extra fields, nonunit coefficients or the other 116 windows follows.

Credit

Credit zxv's receiver-sharing and productive-helper work, Cinna Davis's PR4470, Jacob Alan Sussman, GamingPuzzled's older census and retained native/Clifford/geometry/outer contributors. Prepared for Chris R / Clear1nsight with substantial OpenAI assistance, Apache-2.0. Separate implementations in one session are not independently launched agents, human review or formal acceptance.

Open next questions

Change the length cap, coefficients, adjacency, owned-field allowance or producer/consumer boundary explicitly before reopening this domain. First derive the complete optimistic cost model and test a structurally justified window. A positive relaxed profile in a changed model would still require a geometric realisation and physical/consumer validation. Do not reseed these twelve fixed cases or sum overlapping gains. README.md, TASK.json and the public handoff preserve the scoped exclusion.

[Clear1nsight]

HANDOFF — zero headroom in the declared four-shear domain

Status on 22 October 2026, priority revision 7. Assignment B is complete as a bounded no-headroom certificate at 55b8d34c82fc4df6499c5037e156db6e990b96fe. Final-head registered workflow 39726182814 passes, including onboarding, source authentication, complete enumeration and ceiling checks, canonical receipt comparison, optimised controls and unchanged inputs. The next changed-contract question is unclaimed.

Each of the first twelve PR4470 receiver windows has optimistic gain upper bound exactly zero at C=0.00302015. Every word of at most four unit shears on the same three fields is considered: 22,621 words per sign case, with 84 exact endpoint matches. The dimension relaxation contains every legal monotone common-frame path and retains every exit charge. Even the relaxed costs cannot beat the incumbent. Ten windows have one relaxed profile and two have four, none improving.

This is stronger than merely failing to find a candidate. It excludes strict paid-moment improvement for these twelve fixed windows under this exact alphabet and boundary contract. It does not exclude the other 116 eligible pairs, nonadjacent or longer words, nonunit coefficients, extra fields, changed exits or joint rewrites. Do not add gains across overlapping windows or reseed this excluded domain.

The smallest useful next task is to change one explicit premise and derive its fully charged optimistic bound before a new construction search. Choose one structurally justified case, retain all helper credit and restoration costs, and stop if the new upper bound still has no headroom. A surviving optimistic profile must then be realised geometrically and checked physically; it is not itself a circuit.

Reproduce with python -B scripts/research_package.py --package research/four-shear-window-ceilings. RESULT.json retains every observed scientific field. The original mathematical engine is unchanged; the documented JSON adapter checks all values, types, ordered arrays and fields while normalising only JSON object representation. Six receipt mutation controls supplement the original finite-alphabet and geometric controls.

Canonical main remains f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc, and PR4470 is pinned at b9a13c1673e0e9697de410de16e8bbf3207a7363. The final refresh found PR4535's higher critical-root conditional transfer and PR4534/4539's noncommuting-controller work. Those support changed future investigations, not expansion of this certificate's scope.

Credit zxv, Cinna Davis, Jacob Alan Sussman, GamingPuzzled's earlier census and retained native/Clifford/geometry/outer contributors. Prepared for Chris R / Clear1nsight with substantial OpenAI assistance. No new kappa, upstream PR, merge, frontier update, independent human or formal acceptance is claimed. This fork handoff has not been cross-posted to central CrocSwap#1166 because Discussion-comment writes are unavailable through the current connector.

{"schema":"integer-mult-coordination/v1","kind":"HANDOFF","task":"independent-moment","scope":"Change an explicit scalar alphabet, adjacency, owned-field or producer/consumer premise beyond the certified twelve-window four-shear zero-headroom domain","base":"f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc","expiry":null,"artifact":"https://github.com/Clear1nsight/integer-mult-bounds/commit/55b8d34c82fc4df6499c5037e156db6e990b96fe"}