RELEASED: nonconsecutive C3 gather census remains open

[bitplane]

RELEASED / 2026-10-15T01:52:51.350387+00:00 / priority revision 4.

The nonconsecutive C3 gather census was not implemented or completed before this claim expired. The completed ceiling and fixed-gate entrance checks below were scoping evidence only; no gather result or PR is claimed. On resuming, I refreshed canonical main to 0fdd7d8 and read revision 4. I am retaining the original complex-mechanisms draw and nonce, but taking the explicit P104 shared-space dimension handoff in PR2173 instead. This releases the gather scope for anyone to pursue.

Original claim and source history:

CLAIM — source-pinned nonconsecutive C3 gather screen

Question: can three-source, one-destination gathers across exactly commuting intervening operations reach the original5% selected-word ceiling target, beyond Cinna Davis's consecutive-gather PR1814?

Base c676548106012571fefa1dce0ec16f1bcfe11dce; single OS nonce 04a0b5296b007400a2e6d4c67da47ad2, priority3 complex-mechanisms / complex-new-helper-inventory, scope key f3b0895a4f9f1cc62e75. No reroll. Selected k8 word decompressed SHA256 c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8. The card ceiling and lever controls passed. The fixed-gate entrance scoping probe found no enlargement space and was stopped.

Bounded domain: every A/B triple i<j<k of ADDs with the same destination and three distinct sources, none the destination. There are72469 raw A triples and9417 B triples before restrictions. Right-compact the first two gates immediately before the third in original order. Every actually crossed operation must commute exactly. Recompute all affected frame chains; require legal monotone paths, identical interval boundary frames and the complete ordinary paid histogram unchanged. The gather rank is the sum of every positive destination AND source increment at the three compact gates. Admit rank<=36; centre, early cleanup, terminal paths, coverage law and guard stay fixed. Only schedules with disjoint closed [i,k] intervals are included, avoiding interference between compactions.

Complete favorable bill: replace those priced increments by one rank-sum child, preserving local mass5586 and ideal idle mass1646. All further gather implementation, reads/copies, adapters, helper supply, phase, restoration, precision and hosting overheads are optimistically zero. Before synthesis, the all-noncentre-rank36 envelope {36:2761/18,8:8} has ceiling in ['478089531693/62500000000000', '7649432507089/1000000000000000'], above the unchanged target 35491136290869/20000000000000000. This is planning headroom, not a realizable interface or occurrence claim.

Method: complete candidate census; interval DP with exact rational upper bounds on savings at the declared target (not arbitrary-fixed-exponent ordering of roots); independent subspace/candidate/arithmetic implementation; full scalar/frame replay of the selected reordered word. If the resulting lower bound on the best favorable moment is above one, stop this domain. If a schedule passes, report it only with the remaining physical gather-child obligation. No selected frontier change or new kappa is presumed.

Predecessor credit: Cinna Davis/PR1814 at915bf647756c20a07ab9b8523fe09dfcb4f33f7b for consecutive gathers and this explicit nonconsecutive open question; her PR1865 at939fa9a4aa34fc826ea29d633099d771910adf28 for the opposite shared-source fanout commutation/interval method; PR1764 for tagged joint-child interfaces; Douglas Colkitt/PR1240 and Sagar Thakrar/PR1012 for the ceiling/coverage model; the selected R480/k8 construction lineage. No copied rank sum is claimed to physically implement a native gather.

Entry overlap completely paginated359 open PRs and664 Discussions, no warnings. The targeted gather query returned all8 matches, including the above predecessor/handoffs and no competing exact scope. Metadata search is not a novelty guarantee. Claims/readback and final overlap will be checked before publication.

Expected artifact: one exact screen or candidate with replay, source pins, corruption controls and explicit limits. Claim expires 2026-10-14T19:46:26.986305+00:00. Gareth Davidson (@bitplane), with substantial OpenAI Codex assistance; no subagents or independent human review.