[Clear1nsight]

Change and mathematical scope

Assignment A gives a bounded negative construction result on PR4470's productive-helper word. Among 128 eligible adjacent receiver pairs, only the explicitly selected first twelve were tested, all in phase B. Every selected three-shear replacement preserves the old paid histogram exactly in both orientations and adds one scalar operation. No improvement, new kappa or physical supplier admission is claimed.

For a += ca*x; b += cb*x, set s=-ca*cb and replace by a += s*b; b += cb*x; a -= s*b. The identity holds on arbitrary dirty inputs and for the inverse-transpose word. The checker constructs every feasible contact-dimension triple for this word and independently charges local and complete-word frame movement, including exits. All 408 helper endpoints, main boundaries, warps and centre charges remain fixed. The whole paid profile stays {1:2237,2:388,3:494,4:147,5:36,8:8}.

The separate ceiling submission fork PR18 extends the same twelve-window decision to all endpoint-equivalent words of at most four unit shears. Its stronger result is not a premise of this construction replay.

Task and overlap

Scientific base f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc, PR4470 head b9a13c1673e0e9697de410de16e8bbf3207a7363, priority revision 7. Seven sources are authenticated. TASK.json preserves the original card and declares the user-assigned change to construction. PR4121's earlier T360 census uses different sources and helper contracts. PR4504/4478 verify predecessors rather than this replacement word.

The final refresh found PR4535's higher conditional critical-root endpoint on the unchanged supplier and PR4534/4539's noncommuting-controller work. These do not invalidate the frozen local negative result; the next positive construction must compare against the then-current complete claim, not an obsolete endpoint. Canonical main remains unchanged. Overlap checks were targeted, not exhaustive pagination or proof of novelty. The historical baseline helper was not run.

This fork-only PR targets research/20261022-canonical-base, separating existing CI repairs from its scientific diff. No main merge, upstream PR or selected-record change.

Validation

The first full scientific replay 39723520394 passed at 99f5d3d855a7ad6204072ff021e3621d7c6fa72c on Ubuntu and CPython 3.12.15, standard library only. It includes all twelve exact source windows, both orientations, 21 controls and preservation of committed inputs. RESULT.json retains every emitted field.

Publication head is fe1ff585764663e0310c91b2d4a5dcf09af8e234; its complete rerun is 39726103789. Read that exact-head check for final publication status. Earlier author metadata spellings were rejected before science and corrected to the schema's negative-result; no mathematical predicate was removed.

The unchanged engine's in-memory integer rank keys differ from JSON's required string keys. The registered replay.py authenticates the same engine, freshly executes every original check and compares every field in canonical JSON form. Six additional controls reject changed counts, value types, array order, missing fields and extra fields. It never invokes the authoring --write path or rewrites evidence. See RECEIPT-COMPARISON.md.

python -B scripts/research_package.py --package research/receiver-window-transfer
python -I -O -B research/receiver-window-transfer/verify.py --self-test

No conclusion about the other 116 windows follows. New physical lowering, absolute phases, complete 632-input endpoint, precision/stock, compiler/outer transfer, selected cold replay and optional source-history preflight were not performed.

Credit

Credit zxv's PR4085 dirty-receiver identity and PR4359 productive-helper architecture, Cinna Davis's PR4470 constructor, Jacob Alan Sussman, the fresh-helper/missing-span lineage, Mihir Srivastava, Ryanson Jonathan, GamingPuzzled's earlier census and retained native/Clifford/geometry/outer notices. Prepared for Chris R / Clear1nsight with substantial OpenAI assistance, Apache-2.0. Separate workstreams are not independently launched agents, human review or formal-kernel acceptance.

Open next questions

Do not reseed the same twelve fixed windows. Name an explicit change to the scalar alphabet, adjacency, owned-field allowance or source/consumer boundary, derive its fully charged optimistic moment and test one structurally justified case before expansion. A different source window lies outside this result but still needs a reason to matter. Any later positive candidate needs physical and complete-consumer validation. The package and public handoff preserve these boundaries.

[Clear1nsight]

HANDOFF — twelve receiver windows have no paid-profile improvement

Status on 22 October 2026, priority revision 7. Assignment A is complete as a bounded negative result at fe1ff585764663e0310c91b2d4a5dcf09af8e234. Final-head registered workflow 39726103789 passes, including onboarding, full source-bound replay, exact retained-receipt comparison, original optimised mathematical controls, six receipt rejection controls and committed-input preservation. The next question is unclaimed.

Of 128 eligible adjacent source pairs, only the first twelve were tested, all in phase B. Every selected receiver-sharing replacement retains the exact old paid profile in both orientations and adds one scalar operation. All 408 productive helper endpoints remain fixed. This is not a construction improvement. The separate PR18 expands the same fixed-window exclusion to all endpoint-equivalent words of at most four unit shears. No conclusion about the other 116 windows or changed contracts follows.

The smallest useful next task must name a changed scalar alphabet, adjacency, owned-field allowance or producer/consumer boundary, derive its fully charged optimistic cost, then test one structurally justified source case. Stop if restoration or lost helper credit cancels the gain. Do not merely reseed these twelve fixed windows. Any later positive candidate still needs exact physical lowering, complete arbitrary-input native replay and consumer admission.

Reproduce with python -B scripts/research_package.py --package research/receiver-window-transfer. The scientific engine and frozen inputs are unchanged. Canonical JSON comparison handles integer Python rank keys versus JSON string keys without dropping fields or rounding values. Earlier metadata-enum and receipt-representation defects are disclosed in the package; the final workflow passes without weakening scientific controls.

The canonical scientific base remains f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc; PR4470 remains pinned at b9a13c1673e0e9697de410de16e8bbf3207a7363. The final refresh found PR4535's conditional 0.003020165 endpoint and PR4534/4539's noncommuting-controller work. Future positive constructions should use the current complete comparison point and respect those papers' remaining physical premises. These advances do not change the frozen negative scope.

Credit zxv's PR4085 and PR4359, Cinna Davis, Jacob Alan Sussman, the native/frame contributors, GamingPuzzled's earlier census, Mihir Srivastava and Ryanson Jonathan. Prepared for Chris R / Clear1nsight with substantial OpenAI assistance. This public fork handoff is not an upstream PR, merge, frontier update or central CrocSwap#1166 cross-post. Discussion-comment writes are unavailable through the current connector.

{"schema":"integer-mult-coordination/v1","kind":"HANDOFF","task":"independent-moment","scope":"Change one explicit receiver-word or producer/consumer premise beyond the twelve fixed no-gain PR4470 windows, then derive and test a complete paid budget","base":"f9f85c1e4fa1e955ff39f10fca447e3e2a4e4adc","expiry":null,"artifact":"https://github.com/Clear1nsight/integer-mult-bounds/commit/fe1ff585764663e0310c91b2d4a5dcf09af8e234"}