Conditional κ = 0.001524207950793244: 92-pivot direct504 supplier

[chafreaky]

This raises the conditional saving from #531's 0.001517760977820331 to κ = 0.001524207950793244, exactly 381051987698311/250000000000000000: a 0.42477% improvement in exponent saving. The complex supplier still binds. This is a finite conditional witness under the retained all-size and analytic interfaces.

The construction retains #531's direct-delivery 504-helper architecture and 72 compatible line gauges. A new exact shared-donor selection gives 92 pivots instead of 80. A new whole-owner allocation pays for all changed residual widths. It has 36,288 helper roles, 728 distinct active families per complete invocation, 7,536 remainder children, and no helper banks. Live and physical stock remain 7,168 and 7,682; the global rank deficit remains 2,560.

Quantity	#531	This increment
Kernel pivots	80	92
Width-eight / width-nine helpers	152 / 352	164 / 340
Local paid rank mass	6,240	6,228
Certified complex saving	0.001520068077832496458155	0.001526534707131015364923
Conditional κ	0.001517760977820331	0.001524207950793244

The final global profile is {1:146592,2:55584,3:12464,4:28224,5:7616,6:4032,7:944,48:912}. Both exact moment engines accept the stated complex endpoint and reject the next 10^-24 grid point. Six bootstrap levels and all 47 strict outer inequalities give the displayed κ. The emitted prefix is 225 bits within the retained 512-bit charge.

Reproduction and proof boundary

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

Standard library only, offline, with assertions enabled and a fresh output directory. The fixed verifier runs no optimizer. It rebuilds the raw factory and all rational donor relations, replays both 728-column local orientations, rejects every one of 92 omitted kernel corrections, checks the fourteen source-frontier bases, freshly lowers all 2,924 local phase edges and 224 endpoint adapters, verifies the seven residual wrappers, reconstructs actual physical owners and spectators, recounts the finite invoice, and runs both exact moment engines and the outer assembly.

The unchanged 112-port data controller/data-phase certificate and #493 bit operator remain pinned dependencies. The bit histogram is repriced in both exact engines; its physical operator is not cold-rebuilt here. No cached local phase is accepted in place of fresh lowering. Thirteen local mutations, five wrapper mutations, seven owner/controller mutations and four outer mutations are rejected. Optimized Python, a missing owner map and modified source reject before output creation.

proof/CONSTRUCTION.md, EXPECTED.json, SOURCES.json and MANIFEST.json contain the argument, exact result and file bindings. The entire attributed #531 package is preserved under vendor/pr531. Final frozen-source reconstruction passed on Linux/Python 3.11 and macOS/Python 3.14, with identical canonical-word, emitted-program and local-phase hashes. Receipts are in research/direct504-kernel92-validation/. A Python 3.11 gzip-header mismatch was reproduced as a single metadata-byte difference and fixed by pinning OS byte 255; no mathematical check was weakened. Dedicated CI runs Python 3.11 and 3.14. Remote CI is pending at submission.

Sources and attribution

• Direct delivery with 504 helpers for conditional κ = 0.001517760977820331 #531, icekylinx, with GPT-6 Astra and OpenAI Codex assistance: same-partition direct delivery, 504-helper raw factory, gauge baseline, frame coalescing, and supplier/owner/invoice checkers. Pinned head e07a8a3f9f79c22113398a0c5dbbc7601f489b3e; its package is byte-identical to the initially checked c609855ff92acc8cae3aa0808a4ecb624165f548.
• Punctured Hamming ports for conditional κ = 0.001457945761723368 #523, icekylinx: retained 112-port controller and 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 lineage.
• 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 the preserved source notices: shared-donor kernels and compatible entrance 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 supplier.
• Conditional κ = 0.001469603966017302: rank-sector102 on112 ports, fully rebuilt #529: independent omitted-correction checker, adapted to the actual port count, and its attributed Punctured Hamming ports for conditional κ = 0.001457945761723368 #523 full-phase driver. Its rank-sector construction is not treated as an additive gain.
• 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, phase compilation, exact moments and analytic framework.

The new frozen selection, whole-owner allocation and reconstruction package were prepared for chafreaky with OpenAI Codex assistance. All inherited notices and licenses are retained. No unrestricted optimality, new Lean certification, κ = 1 or unconditional multiplication theorem is claimed.

[Mister-Meeseeks]

Integrated on main in 9449300, with original commit history and individual credit retained.

Your 92-pivot supplier is integrated with the complete package, local phase/endpoint replay, owner audit and exact assembly. Its κ = 0.001524207950793244 is preserved as a reviewed alternative and its mechanism is also used by Rohan’s #536. Your attribution, proof notes, validation package and CI workflow are retained.

Maintainer review and exact scope · Contributor record. The multiplication claim remains conditional on the inherited all-size/realization/analytic interfaces; these checks do not establish a complete unconditional theorem.

Thank you for contributing this work.