Conditional kappa 0.001587480974500277: static44 global admission plus PR542 bit

[rohanarun]

Conditional kappa = 0.001587480974500277, about 0.00085046% above #542. This admits Dugongue #541's local static44 complex appendix into the complete #535 controller, then composes it with our verified #542 bit supplier. The bit supplier now binds again.

The static44 appendix changes the response presentation from 40 to 44 pivots. Our contribution is the global admission: monotone matching of new helper widths to existing whole-owner slots, compaction of actual pending intervals, new residual/spectator charts, and complete finite recount. The global profile is {1:158748,2:52868,3:15160,4:20192,5:4044,6:4048,7:360,8:576,48:1632}. All 36,288 whole-helper roles and every idle remainder are paid; live 7168, physical 7682 and deficit 2560 remain unchanged.

Fresh Python 3.14 verification passes: 728 local columns in both orientations, 44 kernel omission controls, changed scalar/frame and emitted-program checks, 68 fresh exact Clifford edges (2,861 hash-bound unchanged edges reused), residual wrappers, whole-owner/controller audit, seven mutation controls and finite invoice. Global prefix 225 bits; row coefficient 16467 below 20161. The initial role-order digest failure and original failed driver are retained; sorting by actual call time and new helper index repairs serialization without relaxing any check.

Two rational engines give complex b =0.001590416068421022723744 and cited bit c =0.001590005077309865651707. Six explicit bootstrap cutoffs, 47 strict outer inequalities and four invalid-parameter/grid controls pass.

Offline replay (Python 3.11+ and NumPy):
python -B research/static44-r480-composition/verify.py /absolute/new/output

Packaged offline replay now passes on Python 3.11.15 and 3.14.8. Both initial failures and their precise repairs are retained. GitHub CI remains separate; the dedicated workflow covers Python 3.11/3.14. The complete byte-pinned source dependencies and licenses are included. The unchanged PR542 bit operator is cited and repriced rather than rebuilt; unchanged phase/data certificates are explicitly reused.

All inherited all-size compiler, common-label/mutable-source, hosting, precision/tape and analytic-transfer assumptions remain conditional. No unconditional theorem, full Lean proof or measured speedup is claimed.

Prepared for rohanarun with OpenAI Codex assistance. Credits: Dugongue #541 for the static44 construction/proof; icekylinx #535/#531 and phase/compiler ancestry; DreamingOfClouds #484 and R480 #510; eumemic #493; #425/#433 and all authors retained in source notices; our #542 and literal-charge #461/#464/#465/#539 ancestry.

Concurrent #544 reports a higher conditional kappa of0.001588602246663212. This PR improves #542 and is not claimed to lead #544.

[Mister-Meeseeks]

Thank you @rohanarun. This contribution at 77833ffa1110c6645f5d0866ebf41510ee3d27a3 is incorporated in the reviewed family through #588, published in 9594b61.

Admits the local-only static44 response word under a reassigned complete owner map. Sorted helper widths fit the retained slots; actual residual charts and every remainder are recounted. Fresh changed phase edges are checked, while 2861 unchanged local edges and the data controller remain hash-bound dependencies. The separately physically replayed #542 bit supplier is repriced, not silently replaced.

Preserved implementation and research:

• research/static44-r480-composition

The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof.