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Prove a complete-cost obstruction for eight two-accumulator rewrites - #1465
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100-PR batch review at Merged to Reviewed scope: Eight completed two-accumulator recipes pass every one of 256 subset replays. Changed helper endpoints and an all-replica packing dual prove every nonempty use worsens the complex root in this recipe family. Native receipts are pinned predecessor evidence; arbitrary two-accumulator designs remain open. The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions. Batch review, attribution and evidence. Thank you for the contribution. |
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Eight explicit saved-arm rewrites make the two-accumulator escape in PR #1238 concrete on the selected R480 local word. Every subset passes the exact local scalar, frame, entrance, and helper-cone checks. The all-eight word also passes native emission, independent replay, wrappers, and all 2,900 exact local phase edges. The helpers are arbitrary inputs; cleanup and the width-7 to width-9 changes are paid.
Review files: Proof and scope · Evidence · Source pins and credit.
The complete cost excludes an improvement from this method. A signed whole-helper inequality and two strict-majorization arguments prove that every nonempty use has a smaller complex root than the applicable unchanged-word PR #1129 optimum. The result permits arbitrary per-call subsets, every positive replica count, and every owner with the retained capacity stock. The zero-recipe choice attains the family optimum, with inherited conditional kappa
0.001674097969905390. No new kappa is claimed.This proof covers the eight fixed recipes. It does not close the original wider problem of arbitrary partitions, rational encodings, new frame schedules, mixed encodings across packets, or composition with PR #1319. Those boundaries and the failed attempts are explicit. The input is bound directly to the selected PR #1094 replay archive, and the 57,478-state feasible raw frame schedule is retained as a positive control.
Reproduce with Python 3.12 and the standard library:
Expected final line:
PASS_REGISTERED_RESEARCH_PACKAGE research/two-accumulator-saved-arms outcome=negative-result.The package checks all 256 words, the 712-column private-centre scalar interface for the all-eight word, three failure controls, all 1,163 bin patterns by two methods, exact supporting intervals, the baseline attaining table, and both majorization relations. The coordinator independently reproduced the family check and the native local checks. No new global owner stream or complete cold multiplication replay is claimed. Inherited all-size and analytic obligations remain.
Base: bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Source commits, byte hashes, native replay commands, and predecessor notices are in the package. Credit PR #1238, PR #1140, PR #1129, PR #1240, PR #1012, PR #1198, and the retained seven-slot/native lineage. Prepared by Ali Romman (@aliromman) with substantial OpenAI Codex assistance. Apache-2.0.