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Attain the fixed-word packing optimum: conditional κ ≈ 0.0017201008054 - #2863
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…cSwap#2863's shared-kernel words
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…no kappa) Bounded screen of single-helper dirty entry, with every existing gate fixed, on the #2863 (PR2857 shared-kernel) and #2894 (preload-move) supplier words. Exact adjoint responses, full-program frame feasibility, partner cancellation, sub-frame entry, insertions in either phase and one-hop relays with an exact bilinear validity test. Result: 0 frame-feasible candidates on all four words; 8 apparent relays, 0 valid; single-gate and cascade frame refits 0 improving. Calibrated: the same screen gives exactly #2853's 16 quartet helpers on the PR2833 words. With frames relaxed, all 184 eligible helpers are algebraically cancellable, so frame placement is the obstruction; #2894's preload re-synthesis of two zero-frame-first quartets is consistent with this. Also records an independent fast and full cold replay of #2863. Vendored inputs keep their PR2833, PR2857 and PR2894 notices. Prepared for digitalis-p with substantial Claude (Anthropic) assistance; no independent human review claimed. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Combines the complete shared-kernel words from PR #2857 with a width 9 vacancy relay inspired by PR #2856 and five-copy concentration from PR #2848 / PR #2855. The literal T185 construction raises conditional κ to 0.001720100805416885927944 − 10⁻⁴⁶ − 10⁻⁷⁰, an exact gain of 4.176732053326972 × 10⁻⁹ over the full pinned PR #2857 claim.
Adds the ten actual moves, complete owner data, a deterministic constructor, separate source-event and rational moment checks, and a matching exact rational primal/dual across all 1,163 packing patterns. The actual allocation attains the fractional optimum near its moment root for the fixed current native words, helper inventory and bin capacities. The bound applies to every admissible replica count. This closes that packing gap; it is not a maximum over new native words or multiplication algorithms.
Validation: both changed native chains freshly passed all five stages and both orientations on 632 columns. Two unchanged retained chains and the 16-stage parent are explicitly reused from this campaign's fresh four-chain bootstrap. Complete serial supplier/controller, geometry, compiler/precision invoice, BIT and modern outer release passed with source/cache guards and validator predicates retained. A first parallel attempt hit a temporary receipt-read failure; the preserved note explains the serial rerun. The portable wrapper is preflighted separately; its underlying full stages were executed, but a second cold wrapper replay is not claimed.
All inherited asymptotic hypotheses remain. This is informal mathematics and exact finite certification, not Lean formalization or an unconditional multiplication theorem. Credits include Yiyang/Lyy-iiis (#2857, #2848), Marius-Paul Dumitrean (#2856, #2843), Philippe Van Velzen (#2853), Jeremy Kothe (#2833), Dugongue (#2855, #2839) and all retained contributors. Original licenses/notices remain. Root and three Codex agents supplied the new work; no independent human review or global priority claim.
Package:
research/shared-kernel-packing/. Start withREADME.md; runpython -B tools/verify_package.py --work <fresh-external-directory>. Full native/outer replay, exact claim, proof notes and evidence are included.evidence/SOURCE-REFRESH.jsonrecords the latest inspected main/PR snapshots and bounded overlap scope.