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Experimental: add an explicit nonuniform T(509,35,8) cover - #1176

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Experimental: add an explicit nonuniform T(509,35,8) cover#1176
maelcar wants to merge 1 commit into
przchojecki:mainfrom
maelcar:manuel/atlas-nonuniform-turan-35-to-8

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@maelcar maelcar commented Aug 31, 2026

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Summary

  • proves the fixed-asymptotic packing bound: two distinct degree-t sections satisfying the two shared Laurent-coefficient identities agree at no more than 2t-3 finite nonpole points;
  • adds an explicit nonuniform hierarchical T(509,35,8) system with block sizes (177,166,166), thresholds (13,12,12), and exactly 762,054,269,114 selected eight-subsets;
  • records all 305 frozen color patterns, the feasible CP-SAT witness, and two independent exhaustive auditors;
  • provides a false-negative-free candidate-generation reduction for the active t=5 RS-MCA family, subject to separate treatment of singular faces and poles.

Verification

  • primary exhaustive audit: PASS Atlas nonuniform cover blocks=[177, 166, 166] selected=762054269114;
  • independent parser/audit: PASS independent nonuniform cover selected=762054269114;
  • byte-identical replay of the frozen cover and both reports;
  • manifest checked against the normalized Git blobs;
  • optimizer source smoke-tested with the recorded witness as a hint.

Scope

The cover theorem, cardinality, and packing reduction are exact. The recorded optimizer status is FEASIBLE, so this PR makes no minimality or optimality claim. It does not claim the complete d=474 exclusion, a paid Paper-D row, or a leaderboard improvement; those require the remaining singular-fiber accounting and full selected-family execution.

Attribution

Mathematical author: Manuel E. Rey-Álvarez Zafiria.

Add the explicit 762,054,269,114-face hierarchical cover, its fixed-asymptotic packing lemma, and two exact independent audits.
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