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Thank you @chafreaky. This contribution is now retained on main in the scoped 100-PR review and contributor credits. Contribution: Kernel84 construction with an exact packing dual. Review and limits: The optimistic allocation ceiling is restricted to its fixed local word. Later different 92-pivot words are outside it; solver output nominates a dual that is checked exactly. The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions. Reviewed head: |
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This adds a self-contained conditional kernel84 certificate at κ = 0.001389125582984265, plus an exact packing ceiling showing that every whole-helper schedule retaining this local word has κ < 0.001389210509385421. Less than 0.0062% remains through scheduling alone under those stated restrictions.
The construction applies #508's coordinated gauge collapse to #507's partial-own factory and retains all 84 pivots. It reallocates all 40,320 helpers against #508's offset-six call order, then independently checks the literal owner maps, Gaussian phases, normalized spectators, complete controller and finite invoice. The complex endpoint is b = 0.001391057937152176875572; #493's freshly rebuilt bit supplier is nonbinding. No headline gains are added together.
Frontier comparison: #514 subsequently reported κ = 0.001391523459591829 using a different 92-pivot word. This PR does not claim to exceed it. That changed word lies outside the packing ceiling's explicit assumptions. The 92-pivot source reconstruction reproduced its published semantic hash locally; no full #514 replay is claimed here.
The packing bound drops every timing, owner-collision and chart restriction. Its 112 complete integer patterns yield a rational dual checked by both independent moment engines. The checker imports no optimizer and rejects five corrupted certificates. The LP is used only to nominate the dual. This provides a concrete reason to change the local construction instead of extending scheduling searches on this word.
Both cold Python3.14 runs passed on macOS arm64 and Linux aarch64. All seven outer stages,21 dependency stages and13 coordinated-local stages passed on each platform. The complete stable result files are byte-identical:
b5700b468a40f9e142165999b4818a6de0af53183f801b8057c0a40fa78c9c59. Receipts, genuine Boost/compiler checks, guarded physics and exact assembly evidence are attached. GitHub CI is separate and is not claimed passed. The verifier rebuilds both suppliers, the partial-own factory, the coordinated word and all global stages without accepting cached outputs. The source package is immutable; all 328 copied source files were checked against exact Git bytes. The inherited PR507 portability repair pins only two historical floating display annotations, preserving its mathematical and frozen-word hash assertions.Inherited all-size compiler, mutable-basis/common-label transport, Lemma A realization, restored-row, precision/tape and analytic-transfer conditions remain. This is a finite conditional witness and a scoped packing bound, not an unconditional multiplication theorem or κ=1 result.
Credits: eumemic #507/#493; Dugongue #508/#505; Rohan Arun #473's scheduling and flow-capacity work; DreamingOfClouds #484; #496, #495, #501/#502, #458 and the retained earlier authors. New composition, literal allocation, two-platform wrapper and exact packing dual by chafreaky with OpenAI Codex assistance. Licenses, original sources and notices are retained.