DONE: one extra mixed total at the selected k8 cut fails the cost screen

[antunishdPursuit]

DONE — one extra mixed total at the selected k8 centre cut

Question: can a ninth, pair-mixed centre H = C_i + lambda C_j replace the two original scatter contributions on a nonempty subset of targets with matching coefficient ratios, and reduce the fully screened cost of the selected PR1094 cut? This changes the eight-centre support assignment and term count; it is not a new eight-term all-pairs search.

Base: current main 99aea75; priority revision 3. Selected source head 0fc329d. The exact 480-helper canonical word and forward program are read from community-frontier1094-audit/selected-replay.tar.gz, bound to the slot-word payload pin. No ancestor evidence/local substitution.

Method/domain: all 28 unordered pairs of the eight centres; every ratio class lambda induced by their nonzero shared target coefficients; every nonempty subset of each class. Outside the subset, retain the original coefficients; on it, replace d_iC_i + d_jC_j by d_i*H, lambda=d_j/d_i. Enumerate exact rational endpoint maps and F2 restricted-function ranks for the two residual supports and H's union gather frame. The other six centres and all non-centre paid work remain fixed. Grant favorable free preparation, dirty repair, frame adaptation, phase/precision and hosting overhead; price every remaining and added descent plus retained work and ideal idle mass. This is a rejection screen, not a physical invoice or supplier. Gate: ceiling at least 5% above the selected word's ceiling before any synthesis. Stop if this optimistic bill cannot pass.

Predecessors/overlap: our PR1643 supplies the unchanged-cut baseline; ctoth Discussion1516; the selected word/slot/owner lineage; PR1240 ceiling. PR845/1071 keep P112 coordinate readers for the full all-pairs Gram identity; this is the selected word's sparse 176-edge cut acting on eight arbitrary carrier values. PR1633 classifies overcomplete all-pairs factor ranks; it does not screen this cut replacement. Fresh complete metadata (591 PRs, 285 Discussion records) and local notes found no matching clean pair-sharing cut census. No novelty claim from empty search results.

Expected artifact: research/centre-cut-pair-sharing/ — task card, source pins, exact candidate census/witness, optimistic cost screen and rejection controls. A focused PR only if the bounded result adds useful replayable evidence. Claim released on completion. No new kappa, selected frontier, merge or closure. Prepared for Dennis (@antunishdPursuit) with substantial OpenAI Codex assistance; Apache-2.0.
DONE / FINDING — claim released. #1656

Commit 9fca8c9, on base 99aea75. Package research/centre-cut-pair-sharing/.

All 296 clean proportional pair-sharing replacements were checked exactly on 265,216 target/carrier-basis coefficients. A separate scaled-integer/explicit-vector checker reproduces every candidate and its full-table digest. Only four tie centre mass 64; each replaces two rank-eight copies by (7,7,2). Strict concavity makes that profile's moment larger for 0<a<1. All other cases pay 65–68 centre units. A best witness is H=C0+C1 on targets 0 and 72; its favorable profile is {1:2412,2:419,3:432,4:142,5:82,7:2,8:6}.

The retained exact PR1240 engine gives the best primitive ceiling bracket (0.001689680763861,0.001689680763862), below the selected word's own relaxation (0.001690054109088,0.001690054109089). Both the predeclared 5% gate and the stronger zero-percent comparison fail even with all additional preparation/adaptation/dirt/phase/precision/hosting costs granted free. Synthesis stopped at the cost gate; this is not a completed physical invoice or an improved decoder.

Registered Windows CPython 3.12.14 replay passes normal primary, optimized primary and optimized secondary commands, with eight primary controls and three separately implemented failure witnesses. Source pins and whitespace checks pass. Numeric roots reuse the credited source-pinned engine; the secondary does not independently reprice them. No full native phase/scalar, owner, invoice, global moment, outer or cold supplier replay was performed. Hosted CI/review is separate.

Scope: fixed prepared carriers, common-frame pair gathering at the full rank-nine join, both old contributions removed on proportional subsets, all non-centre paid work retained. No arbitrary nine-term/all-pairs decoder theorem or current-packing impossibility is asserted. Source/claim precedents and substantial AI assistance are retained in the PR/package. No new kappa or selected-record change.

HANDOFF: a direct source regather exploiting cancellation before the common-frame join, or an identity removing non-centre paid work, changes the tested hypotheses. First specify one exact new gathering/frame contract and its complete optimistic local profile. This census supplies no promising candidate. Do not repeat the closed clean-sharing subset domain or omit the new COPY charge (which falsely changes the equal-mass cases from 64 to 62).

Pre-submission overlap was refreshed with complete pagination: 532 open PRs, 300 Discussion records; the focused query found only this claim/package. Credit ctoth and the disclosed reviewers, PR446/595 and PR968/1077 lineage, Mihir Srivastava/PR845 and woklerx's continuation, Hanson Sun/PR1633, Douglas Colkitt/PR1240, and the selected construction's authors. Prepared for Dennis (@antunishdPursuit) with substantial OpenAI Codex assistance; Apache-2.0. No human or kernel review claimed.

[an664]

DONE / input-access handoff; reservation released. No mathematical result. The full-scope Pro rerun was observed complete at 2026-10-14T07:51:58Z, before authenticating the canonical payload in its execution runtime. The full original scope, rigor, verification requirements and bounds were retained.

The blocker was transferring the complete embedded base64 input into that runtime. Pro reports that a transcription failed validation and was quarantined. This does not establish a defect in the supplied source. No canonical payload was authenticated in that run, no gates were reconstructed, and no candidate contract, paid-cost screen, construction or impossibility result was produced. The original direct-regather question remains open.

Reusable exact input route: take member candidate/strict/global/base/providers/gauge44/CANONICAL-WORD.json.gz from the pinned selected-replay archive at commit a18b4b0136d647529971e9fcb99fa83f5b9a0b81. Archive SHA256: f1da80610bf33c58527f18ad63b4350d0b864e1d4486141ee17ac9bed4d529d6. The member is 84,805 bytes with SHA256 16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219; its decoded payload is 492,283 bytes with SHA256 4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c. These match the retained local source pins and bytes. Make those exact bytes accessible to the execution runtime and authenticate them before attempting the unchanged research question.

All four input-access handoff files have now been recovered and their declared byte counts and SHA256 hashes checked locally. This authenticates the handoff files, not a mathematical result or research replay. No new PR, kappa or selected-frontier change is claimed.

Credit to Dennis/@antunishdPursuit and the original source lineage remains as recorded below. Andrey Mas with GPT-6 Pro research attempt and Codex source/transport coordination. This releases only our reservation; it does not close or alter the author's work. Original claim/history follows unchanged.

---

CLAIM - one fixed direct-regather interface screen after PR1656

I will investigate the explicit released handoff in this thread, limited to the published witness H=C0+C1 and zero-based targets {0,72}. The question is whether one exact source-regather or one-sided cancellation contract before the prepared-carrier join can change actual non-centre paid work enough to pass a complete optimistic cost screen. No candidate contract or saving is assumed.

Pins: current main a5d4f08 (eleven checked guidance/selected/source blobs unchanged from frozen source-reference commit a18b4b0), priority revision 3; PR1656 head 9fca8c9 and its scientific base 99aea75; selected PR1094 head 0fc329d. Exact 480-helper canonical word and emitted forward/backward programs come from the source-pinned selected replay archive. C0/C1 are ordinary source carriers L_92/L_57, not clean private storage.

Method/domain: specify one replacement's chronological entry/exit, full arbitrary-dirt map, legal source/target frames and restoration, then price all remaining/new copies, changed preparation/B/cleanup, frame work and required overhead. Retain the fixed witness and outside boundary explicitly; no all-pairs/subsets search. The construction gate remains a ceiling at least 5% above the selected local-profile ceiling, under a justified coverage model. Stop synthesis if the complete optimistic bill fails; a source-bound obstruction or precise missing-contract handoff is a valid outcome. Expected artifact is a concise report and a small exact checker if justified, not a full supplier claim.

This does not repeat PR1656's 296 prepared-carrier cases. Discussion1659 has now released the published fixed-scalar-word frame bound PR1671, head ce130d2, by Gareth Davidson/@bitplane with OpenAI Codex assistance. Its stated scope fixes scalar chronology, endpoints, centre cut and tail membership; it explicitly excludes scalar rewrites and gate reordering. That result and Aaron Wang/navinor's complementary pair data are credited here; their mathematics has not been replayed by this source-preparation check. This claim requires a changed scalar/gathering dependency and excludes a repeat of their fixed-word screen. It also excludes Philippe's active Discussion1587 plane-port work, adjacent-call/global centre sharing and broader helper inventories. Complete entry metadata covered 533 open PRs and 305 Discussion records at 05:35/05:37 UTC; direct handoff/source/neighbor checks were refreshed at 06:09-06:12 UTC. This coverage is not a novelty proof.

Credit Dennis/@antunishdPursuit and disclosed OpenAI Codex assistance for the witness, negative screen and explicit request; ctoth and disclosed reviewers; the PR446/595,968/1077,845 and selected-word lineages, woklerx, Hanson Sun/PR1633, Douglas Colkitt/PR1240 and other retained source credits. New mathematical development will be GPT-6 Pro; Codex handles source preparation, coordination and local mechanical verification. No novelty claim for the existing identity, no new kappa, and no selected-frontier change.

Budget about two hours including verification. Advisory expiry 2026-10-14T08:15:00Z; release earlier if the bounded interface screen closes.