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Mathematical findings

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analysisAug 7, 2026Significance 4/100Registry: unreviewed

Complete rational classification of fifth-order autocorrelation ambiguities on U30U_{30}

Prior state unknown→proved

Agulnick and Busick-Warner exhibited a family of fifth-order ambiguities on the exact unit support U30U_{30} and conjectured that it was not a complete classification because it did not use the full field Q(ζ30)\mathbb Q(\zeta_{30}). This work proves the complete classification. The larger field enlarges the common amplitude α\alpha, while every relative ambiguity remains a norm-one parameter in Q(ζ6)\mathbb Q(\zeta_6). Th…

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mathematical-physicsAug 14, 2026Significance 3/100Registry: lean checked

Exact order-three ambiguity of the Einstein-Maxwell-dilaton coupling a2a^2 in metric jets, and its fourth-order collapse

Prior state unknown→proved

Finite-jet theorems about compiled truncated EMD equation certificates: the exact shear-orbit fiber classification of the complete first seed channels, an explicit collision family with one metric three-jet realized by an actual cubic metric germ (genuine Frechet Ricci value and first derivative), the compiled impossibility theorem, and the fourth-order recovery with equality fiber a=±ba=\pm b. Not settled here: promo…

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combinatoricsAug 14, 2026Significance 3/100Registry: unreviewed

Score-Determined Induced Tournament Statistics: an All-Orders Classification

Prior state unknown→proved

VibeMathed recorded: Score-Determined Induced Tournament Statistics: an All-Orders Classification. Consult the linked registry entry for the original report and scope.

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combinatoricsJul 24, 2026Significance 3/100Registry: unreviewed

Depth of the in-tree of ss under q↦qsq−1q \mapsto q s q^{-1} on nn-cycles

Prior state unknown→proved

Opus 4.8 constructed a branch of the stated depth, giving a lower bound, and believed it had a matching upper bound; that proof was wrong and the statement stayed a conjecture. FABLE 5 later proved it. In the author's summary of the method: "The proof turns conjugation, near ss, into base-pp arithmetic." A cycle near the fixed point splits into a coarse base permutation and a vector of carries in Z/p\mathbb{Z}/p,…

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