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[MCA] Route KoalaBear rank-eleven rank-one pair anticodes - #1171

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scottdhughes:codex/kb-mca-rank11-rank-one-anticode-post-1168
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[MCA] Route KoalaBear rank-eleven rank-one pair anticodes#1171
scottdhughes wants to merge 38 commits into
przchojecki:mainfrom
scottdhughes:codex/kb-mca-rank11-rank-one-anticode-post-1168

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@scottdhughes scottdhughes commented Aug 15, 2026

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Summary

Stacked successor to #1168 (exact parent 6a5dcdae1591fc7f044eda6a942bfe178521a48c).

This adds a source-level cross-pair theorem for the post-near affine-error-rank-11 minimizing-pair family. Writing each actual minimizing pair as a 2 x s coefficient matrix (s <= 10), every pairwise-rank-one family is classified into exactly the two bilinear-forms clique geometries:

  • a fixed right factor, giving one affine correction ray;
  • a fixed left factor, giving one affine correction space of dimension at most ten.

Pairwise complete-core overlap K-1 automatically enters this branch by the Reed--Solomon two-polynomial common-root bound.

The fixed-right branch is paid uniformly over every possible universal core. A hostile scope audit caught that the parent complete-ray theorem could not be imported directly when the base minimizing pair leaves identically zero coordinate errors. The repaired common-core-aware affine-ray count scans all 1,048,576 legal core sizes and has exact maximum 8,147,918 at universal core K-1, leaving slack 274,980,728,103,247,169.

For the fixed-left branch, the proper affine-hyperplane arrangement has at most floor(C(n,r+1)/C(m,r+1)) <= 1,031 selected slopes for 0 <= r <= 10. Failure of properness emits an explicit positive-dimensional affine-linear correction component rather than an untyped pair-core terminal.

Scope

  • active-v4 ledger movement: 0
  • KoalaBear closure: no
  • rank-eleven payment: no
  • result: proved structural cross-pair router
  • summation over unrelated rank-one anticodes: not claimed

This removes maximal-overlap pair-core cliques as an unstructured terminal. The residual consists of rank-two pair differences or the emitted positive-dimensional affine-linear correction component.

Verification

  • canonical payload SHA-256: 7190997f4e6e464ce41aa3c8389968985686604ad81e9b272ca7c07130d323a5
  • Python normal and canonical-JSON modes: PASS
  • hostile mutations: 5/5 PASS
  • independent Python implementation: PASS
  • exhaustive Mat_{2 x 2}(GF(3)) maximal-clique control: PASS
  • exhaustive degree-<3 GF(5) common-root control: PASS
  • full 1,048,576-core affine-ray scan: PASS
  • Wolfram exact-integer replay: PASS
  • standalone TeX fragment compile: PASS
  • independent mathematics review: GREEN
  • independent certificate review: GREEN
  • source-scope review: GREEN after repair

Dependency and residual

This PR must integrate after #1168. The source theorem is supplied as an explicit integration fragment; no active source or ledger insertion is claimed.

The strongest next joint after this packet is an aggregate theorem for collections containing rank-two pair differences, or a payment/classification theorem for the emitted degree-one positive-dimensional correction component.

Branch and commit

  • Head: scottdhughes:codex/kb-mca-rank11-rank-one-anticode-post-1168
  • Commit: a3fc2d5aea86577cd50d8b95b6eb2155d4d940f6
  • Exact parent: 6a5dcdae1591fc7f044eda6a942bfe178521a48c

AllenGrahamHart and others added 30 commits August 13, 2026 03:38
@scottdhughes scottdhughes changed the title Codex/kb mca rank11 rank one anticode post 1168 [MCA] Route KoalaBear rank-eleven rank-one pair anticodes Aug 15, 2026
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2 participants