HANDOFF: Joint rank-two child interface candidate (seed 0d762194)

[1337isnot1337]

Status: HANDOFF — conditional local mechanism candidate; no new κ.

Track / seed / task / base. complex-mechanisms; 0d762194a82c097da60f154a08625527; complex-new-helper-inventory; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Selected-record SHA256: 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

Question. Can two tagged one-dimensional register-frame quotients be supplied by one rank-two recursive child at the ordinary rank-two cost? The changed assumption is a new joint interface J2; the full supplier and physical realization remain open.

Bounded construction. On source word SHA256 c2b294300760e1fd6eeab8c22c4d13e4633dca40e52cac8da0d68163a76e3ca8, pair all same-gate one-dimensional climbs in A/B and scheduled early cleanup, then pair terminal one-dimensional transitions by register id. The scan covers 3,451 A gates, 1,846 B gates, 116 scheduled cleanup entries, and 704 terminal registers.

Evidence. The recipe contains 574 gate pairs, 16 early-cleanup pairs, and 163 terminal pairs. Each gate pair is an exact rational shear T_c(x,y)=(x+c y,y) with inverse T_-c; all tagged quotient dimensions equal two. Conditional profile: {1:906,2:1171,3:432,4:142,5:82,8:8}, rank mass 5,586 unchanged. The exact fixed-word ceiling improves by at least 5.241623654% under zero additional interface overhead. At the 5% threshold, only 11 additional rank-one child costs per local call fit if charged against rank-51 idle mass. The relaxation at a=1/99 remains above one.

Submission. Draft PR: #1764. Reproduction and limits are in research/complex-joint-child-seed0d762/README.md; verify.py passes normally and with -I -O, and four negative controls reject. Python 3.12 is unavailable locally, so the registered replay is left to hosted CI.

Open obligations. Prove one legal J2 recursive supplier; price source access, copies, phase/precision transfer, restoration, and complete-call hosting; then test full assembly. No selected result, owner map, or global frontier was changed.

Predecessors / overlap. PR #987/#1094 selected word and owner packing; #1012/#1240 coverage and fixed-word ceiling; #579/#583 single-register frame coalescing; #1348 changed-coverage thresholds. The 09:10 UTC refresh covered all 435 open PRs and 396 Discussions with complete pagination and no warnings; its only broad claim match was expired Discussion #1328, with no exact joint-register child match. The initial claim stayed local while the API was rate-limited; this handoff is posted now that access recovered.

Prepared by Cinna Davis with substantial OpenAI Codex assistance.