Conditional κ = 0.001592518729588709: one call-specific cold-kernel provider

[eumemic]

κ = 0.001592518729588709 (conditional).

This new finite mixed-provider witness exceeds frozen #558 at 060b137c8a6f9d73fd7864c7f8cf2736d6441774 (0.001592517889315014) and the latest #559 at d858c0b2edcc704ef370b3c96dc51a75439b77b0 (0.001592517892053334). Complex b = 0.001595058890747020815446 binds; cited unchanged #543 bit c = 0.001653826988146798944268 remains slack. This package retains the conservative complex fallback charge; #559's separate native-moment correction is not required for this claim.

A five-gate exact dyadic kernel lets one cold helper enter at rank one, shrinking its residual width from nine to eight. Use that complete scalar provider only at stage 4, replica 6, time 52; the other 71 calls retain #558. A literal whole-owner swap enlarges the unique rank-39 idle remainder to rank 40. The full paid difference is e1 + 2e2 - 2e3 + e40 - e39, with unchanged total rank mass. The executable controller serializes both actual provider programs and binds the selected provider at every call and sweep.

Complete profile: {1:166881,2:30530,3:35777,4:13824,5:4032,6:4032,7:208,8:576,40:1,48:1660}. There are 36,288 whole helper owners, no banks, live stock 7168, physical stock 7682, rank mass 520704 and deficit 2560. Each actual provider/orientation's scalar work, coefficient work, paid children and wrappers are recounted; shared compiler reserves use conservative maxima.

Validation:

• Both 728-column scalar orientations restore all 504 arbitrary dirty helper columns and erase private work. Both reflected frame ledgers, all 2929 exact phase edges and 224 endpoint adapters per provider, normalized wrappers and 11 native controls pass. Six new omission controls reject each donor omission and the entire kernel in both orientations.
• Independent mixed controller audit passes all owner-window/chart/spectator checks and 14 corruption controls, including wrong provider dispatch and stale program hashes.
• Fresh complete invoice passes all nine finite checks: prefix 225 < 512, physical row coefficient 16467 < 20161. Actual total scalar real-component primitives are 11,615,712; coefficient work is 5,751,952.
• Two rational moment engines certify the supplier endpoint and reject its next 10^-24 tick. Seven bootstrap levels and all 47 strict outer inequalities certify κ. All 40 malformed-receipt controls and four outer controls reject.
• The final source archive replay passed from scratch under Python 3.12.13 in 216.37 seconds. Python 3.11.5 independently reconstructed and checked the word/phases; its initial binding caught nonportable exploratory gzip headers. The decompressed words were identical. After normalizing the frozen plan, every admission stage passed. The original rejection and correction are preserved. All mathematical assembly fields agree; three run-bound hashes differ with phase-review timing. CI status is separate and is not claimed green.

Reproduce with the Python standard library:

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

Source manifest SHA-256: 0b065a05c8e553278591a7de38137c7f03550b36c6144923ba89ca091d39de1a. Final clean archive SHA-256: c608c977fcfbf9092f3def4130803e77a00604e55572bec5184af385c5e72098. Source, proof, frozen owner/dispatch plan and validation receipts are included. This is a NEW branch and NEW PR; all previous PR heads and claims remain frozen.

Credits and disclosure: prepared for eumemic with OpenAI Codex assistance. Preserves the complete #558 source package and its Dugongue #552, chafreaky #551, icekylinx compiler/controller lineage, #550 assembly, #275 finite-frontier and #543 bit provenance, licenses, notices and AI disclosures. This remains conditional on all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape, analytic transfer and PR543 H1-H5 interfaces. It is not an unconditional multiplication theorem or full Lean certification.

[Mister-Meeseeks]

Thank you @eumemic. This contribution at 210dfa4896e77a8fb5e22ca5a970b0fb0ac984a6 is incorporated in the reviewed family through #588, published in 9594b61.

A helper is made cold only after verifying its exact dyadic dirty-response suffix relation; the complete invocation still has arbitrary initial dirt and inverse cleanup. New owners, reflected programs and phase edges require separate admission.

Preserved implementation and research:

• research/complex-mixed-coldkernel
• research/complex-mixed-coldkernel-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.