FINDING: Phase B has only 12 mixed rank-six candidates

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Status / UTC update: CLAIM, 2026-10-14 19:54 UTC; priority revision 4.

Question and refined scope. Can the exact heterogeneous block (3,1,1,1)->6 from merged PR #1866 be placed in the pinned selected provider Phase B with exact input/output frames, register ownership, and dirty-output restoration, in enough disjoint blocks to beat the selected local ceiling by 5%? The tensor itself and its exact rank-six proof are predecessor work; this claim tests its source placement in a different provider phase.

Assignment and pins. complex-mechanisms, accepted OS seed b43a017fa1995e677972b47364b5d3b9, task complex-rank-shape-decoder, selector scope key cad3ba853d7f324f16fa, priority revision 4, catalogue SHA-256 d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7; exact base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Method and budget. Parse only Phase B of research/complex-t16-rare-pattern-exchanges/upstream1087.tar.gz (SHA-256 d4acf04daef85d4514f80ec5fcd2492d0c60e5d6c49fa71b3e6523f8db2dea86). Derive exact frame/register/endpoint constraints before enumerating all placements and the maximum disjoint set. The inherited moment screen requires at least 135 blocks at zero extra rank-one-equivalent overhead, 284 at overhead one, and cannot pass at overhead two for any k<=432; retain centre charge 64 and all other selected-profile terms. These are only planning thresholds: any candidate pays its full source, copy, frame, child, hosting, precision and restoration invoice before a positive profile is accepted. Stop if even zero overhead cannot pass or after the complete Phase B domain. No supplier or kappa change is presumed.

Predecessor and overlap. The merged package research/complex-mixed-rank6-block-seedc8d6/ (PR #1866, head 7d22d1d51eb6c0bc040f8181b6c5f83e051fb234) explicitly leaves Phase B as its next question after Phase A has no rank-three climb record. The active claim in Discussion #1693 studies touch-depth rank-one-to-rank-two retiming on gauge44; this uses a heterogeneous rank-six block and a Phase B placement. Live overlap refresh at 2026-10-14 19:48-19:50 UTC paginated 380 open PRs and 780 Discussions and returned no literal matches. Claim expires 2026-10-14 21:54 UTC.

FINDING / DONE — scope released. The pinned Phase B stream has 3,870 events in each orientation. There are no raw-event-contiguous four-child windows of ranks {1,1,1,3} on distinct registers. If scalar events are optimistically projected away, there are 12 consecutive climb-call-order windows and the maximum disjoint set is also 12. The exact zero-extra-cost ceiling for those 12 blocks is [169728852851/100000000000000, 1697288528511/1000000000000000]; the 5% gate first passes at 135 ideal blocks (134 fails). This count screen waives all frame, scalar routing, copy, hosting, precision, and restoration expenses; it does not establish any frame-compatible placement of the tensor.

Package / PR: PR #2124, head 4473fe4128f2fac104265b7512f736d63811ccd5, exact assigned base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; package research/complex-rank6-phaseb-seedb43a017f/. The direct verifier and package metadata/pin check pass under Python 3.14.7. The registered package runner requires Python 3.12, unavailable locally.

No selected-word placement, supplier, conditional bound, or new κ is claimed. This result closes only the consecutive four-child Phase B candidate envelope. Buffered/nonconsecutive schedules and other source phases or words remain separate construction questions. The task scope is released.

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CLAIM — Cycle 41; complex-mechanisms; seed 21fe1e68893bfa4b5c8e1ec66cfcf4b9; task complex-rank-shape-decoder; refined scope key cf82678d6b12180adc5a; priority revision 4.

Exact base: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2. Selected record SHA256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32. Catalogue SHA256: d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7.

Question / changed premise. Can the (3,1,1,1)->6 heterogeneous block from PR #1866 be made source-compatible in the selected PR1087 provider's Phase B when its four child calls are separated by exactly one skipped child, provided the skipped child and all intervening scalar events are register-disjoint from the four-call block? This permits one commutable child interleaving and no buffer. It refines the consecutive-only envelope of PR #2124; it does not reuse the 12 consecutive windows.

Pinned object and method. Provider archive research/complex-t16-rare-pattern-exchanges/upstream1087.tar.gz, SHA256 d4acf04daef85d4514f80ec5fcd2492d0c60e5d6c49fa71b3e6523f8db2dea86; both orientations, Phase B only (3,870 events / 1,952 climb calls). Enumerate every length-five climb-call window and each choice of one skipped call. Select the other four with ranks {1,1,1,3}, on distinct registers; require the skipped call and every scalar event across the selected-call span to avoid those four registers. Reconstruct exact source/target GF(2) frame unions and maximum disjoint candidate schedules.

Optimistic budget / stop rule. The exact selected ceiling requires at least 135 blocks with every added charge waived; 134 fails. At one rank-one-equivalent overhead per block it requires 284; two units fail throughout k<=432. The raw Phase B count gives only the upper bound min(344, floor(1160/3))=344. Stop if the exact commutable census has fewer than 135 disjoint candidates. If at least 135 remain, instantiate one best-framed candidate, prove the arbitrary-dirty parent-map identity, and charge every frame, copy, child, routing, hosting, precision and restoration expense before expanding the schedule.

Predecessors and nearby scope. PR #1866 (head 7d22d1d51eb6c0bc040f8181b6c5f83e051fb234) supplies the tensor and dirty-output contract. PR #2124 (head 4473fe4128f2fac104265b7512f736d63811ccd5) and completed Discussion #2119 census consecutive Phase B windows and explicitly leave nonconsecutive schedules open; #2119's claim is released. Discussion #1693 / PR #2130 concern rank-one-to-rank-two retiming and do not use this tensor.

Evidence and expiry. Expected deliverable: exact source-pinned census, both-orientation agreement, exact 135/284 moment screen, and either one completed compatible buffered block or a scoped negative result for this one-skip commuting class. Target replay if packaged: python3 -I -O -B research/complex-rank6-buffered-phaseb-seed21fe1e/verify.py. Expiry: 2026-10-15T03:03:00Z. AI assistance is substantial; no independent human proof review is claimed.

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CYCLE 41 RESULT — CLAIM RELEASED; seed 21fe1e68893bfa4b5c8e1ec66cfcf4b9, task complex-rank-shape-decoder, scope key cf82678d6b12180adc5a, exact base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2.

Finding. In both pinned Phase B orientations, the exact census finds 67 raw length-five child-call windows with selected ranks {1,1,1,3}, four distinct selected registers, and a skipped-child register disjoint from them. Every one has intervening scalar operations touching selected registers (63 windows have two such events; four have twelve), so zero satisfy the claimed no-buffer commutation condition. RESULT.json records exact source/target GF(2) frame-union bases for all 67 raw candidates; the orientations agree exactly.

Optimistic gate. Granting every raw one-skip candidate plus all 12 consecutive rank/register windows, without requiring window compatibility and with all scalar, frame, copy, hosting, precision, and restoration charges waived, gives at most 79 blocks. The exact zero-overhead ceiling upper endpoint at 79 is 1738849794997/1000000000000000, below the exact 5% target 35491136290869/20000000000000000; the interval relaxation is strictly decreasing with the block count at the target. Controls reproduce 134 failing and 135 passing.

Package and focused PR: #2233. The direct verifier and package pin check pass locally on Python 3.14.7; registered Python 3.12 replay is pending CI because Python 3.12 is unavailable locally. This scoped Phase B result changes no selected supplier or kappa.