Conditional κ = 0.001592584727281865: three complete complex providers and reassigned owners

[eumemic]

κ = 0.001592584727281865 (conditional).

This replaces the homogeneous PR558 invocation choice with 15 zero-pivot, two four-pivot and 55 eight-pivot complete providers. Eighteen literal whole-owner reassignments eliminate all 128 rank-one idle remainders. The complex rate is b = 0.001595125099152880684647; unchanged cited PR543 gives c = 0.001653826988146798944268, so complex binds. A separately verified conservative complex recurrence gives κ = 0.001592584724544791.

The complete paid profile is {1:166496,2:30784,3:35907,4:13696,5:4032,6:4032,7:208,8:576,39:1,48:1660}. The full controller binds each actual provider and reflected program to all 72 calls, checks 36,288 literal whole-owner roles, and reconstructs 3,018 orthogonal chart types and 4,240 positive idle remainders. Live stock 7168, physical stock 7682, rank mass 520704, deficit 2560; no auxiliary banks.

The native exact-complex recurrence credits rohanarun's PR559. The exact Clifford programs and full orthogonal cover introduce no exceptional complex residue classes, so only the generic complex surcharge is removed. PR543's bit fallback remains charged. The package retains and verifies the conservative recurrence first; all scalar/Horner, wrapper, phase, group/router, precision, tape, row and idle charges remain.

Validation: complete source and clean archive replays with Python 3.11.5 and 3.12.13; all 728 scalar columns in both orientations, 504 arbitrary dirty helpers restored, both reflected frame ledgers, 2929 exact phase edges and 224 endpoint adapters for every provider, normalized wrappers, promotion/native omission controls, 14 controller mutations, 50 malformed assembly controls, a fresh complete finite invoice, both rational moment engines with adjacent supplier endpoint rejection, seven bootstrap levels, 47 strict outer constraints, four outer controls and two recurrence controls. GitHub CI status is separate from these local receipts.

python3 -B research/complex-mixed-048/verify.py --work /tmp/mixed-048-replay

The self-contained source uses only the Python standard library; assertions are required. Portable gzip normalization changes metadata only. Validation receipts and the source archive digest are recorded in research/complex-mixed-048-validation/.

Provenance: unchanged full PR558 (060b137c8a6f9d73fd7864c7f8cf2736d6441774) and PR559 (d858c0b2edcc704ef370b3c96dc51a75439b77b0) packages and their notices/licenses are preserved. The mixed controller derives from PR561 (210dfa4896e77a8fb5e22ca5a970b0fb0ac984a6); underlying Dugongue PR552, chafreaky PR551, icekylinx compiler/controller and other ancestry remains credited. PR543 is cited unchanged, not claimed freshly replayed here. This new construction, code, review and packaging were prepared with OpenAI Codex assistance; prior authors' AI disclosures are retained. All previously published PR heads and claims remain frozen.

Scope remains conditional on inherited all-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, analytic transfer and bit H1–H5 contracts. This is finite exact evidence, not an unconditional multiplication theorem, full Lean certification or practical speed claim.

[Mister-Meeseeks]

Thank you @eumemic. This contribution at 27070553cfbf094148a74170481738f8b747d82e is incorporated in the reviewed family through #588, published in 9594b61.

Zero/four/eight-pivot providers are literal alternatives at complete calls. Reassigning eighteen owners removes small remainders only after each owner window is checked; no interpolation between providers is used.

Preserved implementation and research:

• research/complex-mixed-048
• research/complex-mixed-048-validation

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.