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Result: exact optimum of the selected PR1094 structural simultaneous-axis assignment relaxation. Nine checked compatibility patterns cover all 1,792 groups and 4,866 eligible children; independently checked integral flows enumerate all 1,049 labelled rank vectors (795 feasible). The attaining ranks minimize the formal moment for every real 0<a<1. Native relaxation price 0.001673074238324615; NO improved kappa claim.
The attaining overlay fails actual eight-stream composition at replica 0, port 0, identity cover, Fourier character 32. Baseline iI becomes a matrix differing at (Y0,Y0), (Y1,Y0) and (Y3,Y3). A single axis-32 move from child 8 to child 12 also fails. Both pass the structural conditions, while the new exact Gaussian-integer guard rejects them. Actual emitted chronology and all 30 relevant hosted occurrences are included. The inherited controller/invoice/assembly accepts the invalid optimum even with its 15+69+12 controls.
Credit: PR1324's closure at 2026-10-13 23:22:57 UTC had already acknowledged the same cross-family issue and credited Rohan Arun. We credit that prior finding, plus Gonzalo-Mier PR1252 and Guéorgui Maissouradze / PatatePatatePatate PR1276 for the overlay/star/ceiling lineage. This contribution adds the complete selected structural optimum, explicit matrices and reproducible regression; no priority claim for the underlying flaw.
Validation: registered full replay and eight test groups pass on Python 3.12.3; a read-only isolated Python 3.14.4 full replay has identical receipt ced1a8f99c9ac6c3f4ea31c5f13c7226ce1735db1e1cbca3417c0e72a88e9d28. All inputs remain unchanged. The final GitHub head and all 17 files were checked. Local/native and bit artifacts were authenticated and reused; no complete ancestry rebuild or Lean proof is claimed. Hosted CI is separate.
Handoff: characterize the exact operator-preserving subdomain with typed stream identities, and use the one-axis witness to repair broader controller admission. This result does not prove that every nontrivial assignment or every assignment at the optimum histogram is invalid. No selected record or predecessor package was changed.
One OS selection 3dc042161f3eb4eb1e4768c6bbc6e12f, selected-packing, scope key 2eb6f6918b10e182033b; base bce54fb. The scope changed from attempted construction admission to exact relaxation plus obstruction in response to a failed semantic test, without rerolling. Gareth Davidson (@bitplane), substantial OpenAI Codex assistance; no subagents or independent human review. Claim released as complete.
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DONE — PR1387
Artifact: #1387
Package: research/selected1094-idle-reassignment/
Mathematical commit: 28b898f
Final submission commit: 1d427e0
Result: exact optimum of the selected PR1094 structural simultaneous-axis assignment relaxation. Nine checked compatibility patterns cover all 1,792 groups and 4,866 eligible children; independently checked integral flows enumerate all 1,049 labelled rank vectors (795 feasible). The attaining ranks minimize the formal moment for every real 0<a<1. Native relaxation price 0.001673074238324615; NO improved kappa claim.
The attaining overlay fails actual eight-stream composition at replica 0, port 0, identity cover, Fourier character 32. Baseline iI becomes a matrix differing at (Y0,Y0), (Y1,Y0) and (Y3,Y3). A single axis-32 move from child 8 to child 12 also fails. Both pass the structural conditions, while the new exact Gaussian-integer guard rejects them. Actual emitted chronology and all 30 relevant hosted occurrences are included. The inherited controller/invoice/assembly accepts the invalid optimum even with its 15+69+12 controls.
Credit: PR1324's closure at 2026-10-13 23:22:57 UTC had already acknowledged the same cross-family issue and credited Rohan Arun. We credit that prior finding, plus Gonzalo-Mier PR1252 and Guéorgui Maissouradze / PatatePatatePatate PR1276 for the overlay/star/ceiling lineage. This contribution adds the complete selected structural optimum, explicit matrices and reproducible regression; no priority claim for the underlying flaw.
Validation: registered full replay and eight test groups pass on Python 3.12.3; a read-only isolated Python 3.14.4 full replay has identical receipt ced1a8f99c9ac6c3f4ea31c5f13c7226ce1735db1e1cbca3417c0e72a88e9d28. All inputs remain unchanged. The final GitHub head and all 17 files were checked. Local/native and bit artifacts were authenticated and reused; no complete ancestry rebuild or Lean proof is claimed. Hosted CI is separate.
Handoff: characterize the exact operator-preserving subdomain with typed stream identities, and use the one-axis witness to repair broader controller admission. This result does not prove that every nontrivial assignment or every assignment at the optimum histogram is invalid. No selected record or predecessor package was changed.
One OS selection 3dc042161f3eb4eb1e4768c6bbc6e12f, selected-packing, scope key 2eb6f6918b10e182033b; base bce54fb. The scope changed from attempted construction admission to exact relaxation plus obstruction in response to a failed semantic test, without rerolling. Gareth Davidson (@bitplane), substantial OpenAI Codex assistance; no subagents or independent human review. Claim released as complete.
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