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Conditional κ = 0.001720184528377469: two more staged quartets on #2863's shared-kernel words - #2894
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Oct 16, 2026
…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>
This was referenced Oct 20, 2026
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Summary
Conditional κ = 0.001720184528377469533073999999999999999999999899999999999999… (70 decimals; the exact value is
kappainresearch/shared-kernel-packing/outer/OUTER-CLAIM.json, SHA-256 of the decimal string8484bef1e0871b2983ca09bc32d47b1eb9ffe1705dba106fa673561a5c425933). This package keeps PR2863's (Dugongue) shared-kernel words (PR2857, Lyy-iiis) and adds, as a declared source-bound stage, two more staged quartets (456,457,466,467) and (458,459,464,465) obtained by preload re-synthesis: per call the paid profile changes by {1:+10, 3:-4} and the helper inventory becomes {8:86, 9:232}. A residue-free T74 owner fill (two interleaved copies of the T37 chronology, 666 calls, idle {1:17316, 3:6327, 5:8547, 48:26825}) packs the new inventory. Fresh native chains for both changed words, complete admission and the modern outer release pass; exact kappa = 0.001720184528377469533074 - 1e-46 - 1e-70, above PR2875 by 8.37229605836e-8 and above PR2863/PR2857. No optimality certificate is claimed for the new inventory. Inherited all-size hypotheses remain.Verification
Fresh checkout of
9e291aab43b6dee08a5702b69d7ab2d140dd1bbf. Manifest:3d6d245089a2080daaae932f0919bb9bd420a45c5fb08534231af1fedcda88cc.PASS package manifest: 171 files
Package manifest; exact gates against PR2827, PR2833, PR2843, PR2848, PR2853, PR2857, PR2863 and PR2875; tools/ci_verify.py (declared-stage re-application, independent owner/moment/profile checks); materialize_source.py (exact 541-file PR2833 source from Git objects); reproduce.py: derivation of the declared preload-move stage with its independent reviewer and fault controls, fresh native preparation of the two changed words, fresh retained bootstrap, complete replica admission and the modern outer release. Conditional kappa 0.0017201845283774695330739999999999999999…(70 digits).
Full package-owned verification passed in 907.44 seconds. The fresh receipt binds the exact package manifest and score.
See
research/shared-kernel-packing/README.mdfor reproduction commands and proof qualifications.Credits
PR2863 (Dugongue): the construction package this builds on, credited first. PR2857 (Lyy-iiis, Yiyang Lu) and PR2848 (Lyy-iiis): the staged shared-kernel words, owner/replay tooling and portable admission. PR2843 (mdumitrean): allocation/owner-flow lineage. PR2853 (philippeVV): dirty A-phase entry. PR2839 / PR2827 / PR2824 (Dugongue), PR2833 (Jeremy Kothe, jeremykothe2, with AI assistance) and the inherited lineage. Ours (Jeremy Kothe (jeremykothe2), with AI assistance): the two extra staged quartets (456,457,466,467) and (458,459,464,465) found by preload re-synthesis (PreloadMove), declared as a source-bound stage with independent review and fault controls, and the residue-free T74 owner fill.
Update (text-only follow-up, head 18d03c4)
The files in
research/shared-kernel-packing/evidence/come from a development run ofreproduce.pywith a prepared retained-native cache (--prepared-retained), not from the no-cache release runs;evidence/README.mdnow says so. The complete no-cacheverify_release.pypassed separately on Windows (957 s) and on WSL Ubuntu-24.04 (646 s), and again from the new head on Windows, with the identical kappa. The only changes areevidence/README.mdand itsMANIFEST.jsonentry (172 files).