Conditional κ = 0.001530327580902932: kernel92 with native-body frame lifts

[chafreaky]

This composes #533's 92-pivot supplier with #534's native-body frame assignment. The complete emitted construction certifies conditional κ = 0.001530327580902932, exactly 382581895225733/250000000000000000: 0.40150% above #533 and 0.42647% above the pinned #534 snapshot.

The constructor first rebuilds #531's raw 504-helper factory and #533's exact rational kernel selection. It matches the native A/B scalar operations against #534's frozen word and transfers their 662 frame lifts. The new kernel prefix, helper entrances, target levels, center cuts and cleanup stay fixed. Every transferred frame contains its raw constructor frame and every register chain is checked independently. This is a proved compatibility of the actual words; the source PR exponent gains are not added.

The local profile becomes {1:2174,2:496,3:357,4:226,5:139,6:56,7:8}. Its rank mass remains 6,228. The 164 width-eight and 340 width-nine helpers, 36,288 whole-owner roles, 7,536 idle remainders, 7,168 live families and 7,682 physical families are unchanged from #533. The final global profile is:

{1:156528,2:35712,3:28376,4:16272,5:13592,6:4032,7:944,48:912}

Both exact moment engines accept b = 0.001532673072778713292743 and reject the next 10^-24 grid point. The complex supplier remains binding against the unchanged #493 bit rate 0.001565442026981656908596. Six bootstrap levels and all 47 strict outer inequalities give the displayed κ. The fresh prefix is 225 bits within the 512-bit charge, and the global rank deficit remains 2,560.

Concurrent work: #536 independently publishes the same composition, local profile and rate. This PR retains its separately rebuilt cross-platform receipts and transfer controls. #535 now reports the stronger conditional κ 0.001584931111785787; this PR is below that newer claim. The #534 comparison above uses pinned commit 768183a86a8c961621702547042579eb9f376c2c, before its later frame-search update.

Reproduction and validation

python -B research/direct504-kernel92-lifts/verify.py /tmp/direct504-kernel92-lifts-check

Standard library only, offline, with assertions enabled and a fresh output directory. No optimizer runs. The verifier rebuilds the fixed supplier, independently checks the transfer, replays both 728-column local orientations, freshly lowers all 2,924 local phase edges and 224 endpoint adapters, verifies seven normalized residual wrappers, re-emits the actual whole-owner program, recounts its complete finite invoice and runs the exact exponent assembly.

Controls reject 92 omitted kernel corrections, 13 local corruptions, five wrapper corruptions, seven owner/controller corruptions, four frame-transfer corruptions and four outer corruptions. Optimized Python, missing owner data and modified source reject before output creation. Portable gzip output pins level nine, mtime zero and OS byte 255; no mathematical tolerance is introduced.

proof/CONSTRUCTION.md, EXPECTED.json, SOURCES.json and MANIFEST.json bind the construction. The final source passed on Linux/Python 3.11 and macOS/Python 3.14, with matching canonical-word, emitted-program and local-phase hashes. Receipts are in research/direct504-kernel92-lifts-validation/. Dedicated CI runs Python 3.11 and 3.14; remote CI is pending at submission.

Sources and scope

• Conditional κ = 0.001526158885117467: frame-chain search on #531's 504-helper word #534, rohanarun with Claude Opus 5.5 (Anthropic), 768183a86a8c961621702547042579eb9f376c2c: the selected frame assignment and independent monotone-lift checker. The new frame optimization is credited to that work.
• Conditional κ = 0.001524207950793244: 92-pivot direct504 supplier #533, chafreaky with OpenAI Codex assistance, ae63ec50f99862efeda351e7687b087744423521: the 92-pivot selection, unchanged owner map and full-phase reconstruction framework. Its later merge head 66b00aeaabb6b4b0545b65685c1ea78f157a8d5e preserves the proof package bytes.
• Direct delivery with 504 helpers for conditional κ = 0.001517760977820331 #531, icekylinx with GPT-6 Astra and OpenAI Codex assistance, e07a8a3f9f79c22113398a0c5dbbc7601f489b3e: direct delivery, same-partition source frontier, raw 504-helper factory, gauge baseline, frame-coalescing argument, and supplier/owner/invoice checkers. Its entire package is preserved under vendor/pr531.
• Punctured Hamming ports for conditional κ = 0.001457945761723368 #523, icekylinx: 112-port controller/restriction ancestry. Conditional kappa 0.001391523459591829: partial-own factory, 92 pivots and asynchronous whole owners #514, Dugongue, and κ = 0.001363614743745701: partial-own factory with 84 kernel pivots #507, eumemic: packet and partial-own ancestry. Asynchronous whole-owner replicas: kappa 0.001357701757628940 (+1.9236% over #496) #505, Dugongue: asynchronous scheduling. E8 bit supplier c ≈ 1.044064·10⁻³ in the nine-stage word (+2.2 % bit cap; no new κ, complex-bound) #417/Split centres and source-basis reuse for conditional κ = 0.001120864952258278 #433/κ = 0.001128832830332521: #417's shared-donor kernel on #433's R758 bit word (+0.71%) #435/Conditional kappa 0.001249035299298004: hosting-selected rank147 kernel #434/κ = 1.136403735815528e-3: R740 shared-donor kernel with 57 primitive frame changes #440/Complex supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas) #484 and preserved notices: exact response kernels and gauges, including DreamingOfClouds's implementation with Claude Opus 5.5 assistance. Conditional κ = 0.001303530097714685: an E8 bit word with 489 helpers, sources as carriers (0.001325 with #484's draft complex supplier) #493, eumemic: unchanged bit operator.
• Conditional κ = 0.001469603966017302: rank-sector102 on112 ports, fully rebuilt #529 and its attributed Punctured Hamming ports for conditional κ = 0.001457945761723368 #523 reference: independent omitted-correction checker and full local-phase driver. κ = 1.048005508028206e-3: mutable-basis Hamming packets (≈2^-9.89814; conditional; complex +4.97%) #425/Split centres and source-basis reuse for conditional κ = 0.001120864952258278 #433/κ = 8.75481145306751e-4: first E8 bit word (complex-bound; +9.29% over #352) #370/Conditional κ = 8.04849251275843·10⁻⁴: post-Design-T kernel, retiming and reorders on #357's reordered base word with all 471 twins (+0.0679 % over #359) #361/Conditional κ = 7.64230861320245e-4: the paired-cube bit word at cube size p = 10 (h = 20, m = 100), with a new centre-sharing complex supplier (+1.21% over #314) #315 and credited predecessors: geometry, phases, exact moments and analytic framework.

The transfer, compatibility controls and combined reconstruction were prepared for chafreaky with OpenAI Codex assistance. All inherited notices and licenses remain intact.

The unchanged data-controller/data-phase certificate and #493 physical bit operator remain pinned dependencies; the bit histogram is repriced but its operator is not cold-rebuilt here. All local phases are fresh. All-size compiler, common-label/mutable-basis realization, normalized Lemma A, restored-row, precision/tape and analytic-transfer interfaces remain conditional. No new Lean, unrestricted optimality, κ = 1 or unconditional multiplication claim is made.

[Mister-Meeseeks]

Thank you @chafreaky. This contribution at a1460516226555dd375d9adb82a8e1dcbfe1ca79 is incorporated in the reviewed family through #588, published in 9594b61.

Transfers 662 frozen native-body frame lifts onto the raw 92-pivot constructor by exact scalar-gate identity. Each lifted frame contains its raw constructor frame; every actual chain, phase edge and owner is checked. New kernel/entrance/cut/cleanup boundaries are fixed. Gains of the two parents are not added. Fresh changed supplier replay passed; PR493 bit and unchanged data-phase certificate remain pinned dependencies.

Preserved implementation and research:

• research/direct504-kernel92-lifts
• research/direct504-kernel92-lifts-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.