Conditional κ = 0.001677380107853623: idle rank-48 axis reassignments with simultaneous swaps toward rank 51 on #1305's four cold kernels

[jeremykothe2]

Summary

Conditional κ = 0.001677380107853623. Extends #1305's multi-donor idle exchange to simultaneous axis reassignments (swaps) inside each replica/port group: rank-48 idle children exchange axes so that the 4-child groups reach (51,51,51,39) instead of (51,51,48,42), 3-child groups (51,51,42), and (51,51,45,45)/(51,48,45)/(51,45) as before. Idle H48=11374 becomes H39=1530, H42=244, H45=1477, H48=1568, H51=6555 with every group's axis multiset, owners, dispatch and native words unchanged. The frozen move list (SWAP-MOVES.json.gz, found by an exact CP-SAT search) is not trusted: verify_idle_overlay.py recomputes every legality condition from the final axis lists (moved axes commute with all stage X/Y, terminal Y and src/dst translations; every final child orthonormal and independent, rank at most 51; group axis multiset unchanged; X2 family disjointness), seven illegal-swap controls are rejected, and check_emitted_operator.py proves exact equality of the emitted per-port operator (T and the Z4 phase form, chronology included) with direct evaluations; then the overlay-aware audit, invoice, strict assembly, 114 admission and 12 bit controls.

Verification

Fresh checkout of 43c19465dc7fd89b991612887c2cdb5ccf57925e. Manifest: 348050b317feb128b3db4f98da363326ac8162792fa073a46c9c90a7c283bf19.
PASS package manifest: 103 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 0.001677380107853623

Full package-owned verification passed in 66.19 seconds. The fresh receipt binds the exact package manifest and score.

See research/global-mixed-four-cold-kernels-idle-swaps/README.md for reproduction commands and proof qualifications.

Credits

Base: #1305 (jeremykothe2; #1297 rohanarun four helper-donor cold kernels, #1274 pivot 531, #1286, #1218/#1193/#1148 construction). Idle exchange method and overlay-aware audit: #1252 (Gonzalo-Mier); star ceiling analysis #1276 (PatatePatatePatate); packing-cap analysis #1240/#1264 (Mister-Meeseeks); X2 disjointness audit #1312 (navinor); phase criterion #1255 (bitplane). Research direction, prioritisation and release strategy: jeremykothe2. Implementation assistance: oh-my-pi.

[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.