κ = 0.001363614743745701: partial-own factory with 84 kernel pivots

[eumemic]

κ = 0.001363614743745701

This conditional whole-owner construction improves frozen #501 by approximately 1.496%. It combines the unchanged #493 R489 bit supplier with a new complex factory that loads 112 own-block helpers from existing rank-two pair intermediates. The changed invertible partial bases remove 56 factory operations and admit 42 more kernel pivots: 80 gauges and 84 pivots now give entrance rank 190.

The complex endpoint is exactly b = 1365476727944167989749/10^24. Frozen retiming and a newly emitted pooled owner allocation give the assembled value κ = 1363614743745701/10^18. All 40,320 helper roles occupy whole physical families, with 800 distinct owners per complete invocation. Live/physical stock is 7,680/8,258, and the complete paid profile is:

rank   1       2      3      4     5      6     7     8     32  48
count 179832  16128  40655  6048  24343  4608  1128  3112   1 369

Every rank-32 and rank-48 idle remainder is paid. The rank deficit remains 2,496; strict halving is 73² > 2·48². The full scalar/Horner invoice, physical stock, global prefix, two rational moment engines, six bootstrap levels and all 47 outer inequalities are recomputed.

The package is research/r489-partial-own-kernel84/. It rebuilds both pinned suppliers, the new factory and selected kernels, an unretimed canonical comparison, the retimed scalar words, exact phase recipes and paid wrappers, then the actual whole-owner controller. Independent checks cover all 28 own-tetrad bases, all 84 kernel relations, all 800 scalar columns in both orientations, arbitrary dirty restoration, both 25,290-event frame ledgers, 3,924 actual orthogonal 73-column maps, 18 controller rejection controls and 14 Lemma G necessity controls. Guarded physical simulations check all 2,947 used transitions on 512 columns and both full orientations on 890 structured/random basis columns plus eight dense columns, with bounds before integer operations execute.

python3 -B research/r489-partial-own-kernel84/verify.py /absolute/fresh/output \
  --boost-include /path/to/boost/headers

Requirements: Python 3.14, NumPy, SymPy, Bash, a C++17 compiler and genuine Boost headers. No network or optimizer is used for verification. MANIFEST.json binds the package and SOURCE.json retains all 266 original supplier-file hashes. Historical records under provenance/ describe the #496/#501 ancestry; the new candidate's acceptance comes from the fresh verifier and EXPECTED.json.

This retains the inherited all-size compiler, mutable-basis/common-label, Lemma A realization with borrowed spectators, restored-row, precision/tape and analytic-transfer contracts. Finite checks and sampled end-to-end physical tests do not establish those all-size contracts or an unconditional multiplication theorem. The comparison is within the stated whole-owner interface. The newly updated #473 separately claims κ = 0.001371428043382419 through nonuniform asynchronous whole-owner scheduling; this PR is a fully replayed improvement over frozen #501, and does not claim to exceed that newer number. Its changed local factory and kernel selection are independent ingredients for further scheduling experiments. Larger draft numbers using cross-family splits carry separate proof obligations.

Credits: eumemic (#493), DreamingOfClouds (#484, with Claude Opus 5.5 assistance), DaysSky, icekylinx, chafreaky, Zhihao Chen, Rohan Arun, Dylan Crow, Jacob Sussman and the authors retained in the pinned notices. This new factory, kernel selection, retiming, allocation, audits, integration and documentation were prepared with substantial OpenAI Codex assistance. Original Apache-2.0 licenses and AI disclosures are retained. This is a new branch and PR; #496, #501 and every previously published head and claim remain frozen.

Validation: both complete fresh Python 3.14 source and committed-archive replays finished with observed exit 0. Every scalar, reflected-ledger, physical, owner, invoice, exact-moment and outer-assembly admission passed. The package manifest SHA256 is 1a84b876ecc3247ffbda8c85f08fe91ff6369a7b81f1b972b7108f827ae5defc; both replays produce exact-math SHA256 90fd7d912c39187a6402e76d83e36f1cf2880a20e565a2c7c782bf19c3cc1f6c. All 314 package files were compared with committed blobs. This reports local fresh verification, not GitHub CI success.