Conditional κ = 0.001676021619355108: #1252's idle pair exchanges on #1218's global mixed X54 + fusions construction

[jeremykothe2]

Summary

Conditional κ = 0.001676021619355108. Applies Gonzalo-Mier's idle pair exchange from #1252 (completely idle rank-48 child pairs 48+48 → 45+51, same axis union, so the exact phase polynomial, owners and dispatch are unchanged; halving guard 73² > 2·51²) to #1218's construction. 4,781 disjoint pairs: idle H48 = 11374 becomes H45 = 4781, H48 = 1812, H51 = 4781. Local words, owners and dispatch are unchanged; the overlay-aware controller audit, invoice, strict assembly and admission/bit controls are rerun. +2.12×10⁻⁷ over #1218 (0.001675809683500501).

Verification

Fresh checkout of bfc7806e5aee389b5bea1ee1f559684f031db702. Manifest: aa0936a88a00f0eda14331177195d571fe14d7c86d519a5f8c02915ae912c8ba.
PASS package manifest: 98 files

Fresh native replays of both provider words (phases step edge-parallel, byte-identical output; with --native-cache a word whose hash-checked completed replay is cached reuses it), then the package's own verify.py (literal words, independent local audit, fusion/X54 controls, leaver premise, literal construct, strict global admission): PASS_GLOBAL_MIXED_X54_IDLE_EXCHANGES_NATIVE_AND_STRICT_ADMISSION 0.001676021619355108

Full package-owned verification passed in 207.5 seconds. The fresh receipt binds the exact package manifest and score.

See research/SET-ME/README.md for reproduction commands and proof qualifications.

Credits

Mechanism: #1252 (Gonzalo-Mier), idle pair exchanges and its audit/assembler patches. Construction: #1218 (rohanarun) and #1193 (jeremydiviney), global mixed allocation with X54 and source-holder fusions, on #1148 (tomdif) joint entrances, #1195 fusions and #987/#1225 X54; packing-ceiling analysis #1240/#1264 (Mister-Meeseeks). Further inherited sources are in the package notices. Research direction, prioritisation and release strategy: jeremykothe2. Implementation assistance: oh-my-pi.

Note: the package directory is named research/SET-ME in this commit due to a packaging slip; a follow-up will rename it without changing any verified content.

[jeremykothe2]

Closing: this result is invalid. Its idle-overlay step moves axes between idle children of different (pair, side) families. The retained DATA-PHASES recipes (data_phases.py, exact_child) fix each family's Z4 multiplier, and every changed child here alters its family's multiplier, so the claimed κ is not supported. Thanks to rohanarun (#1286) for flagging the overlay problem. The overlay mechanism inherited from #1252 has the same issue. Our overlay-free results (#1261, #1274) are unaffected.