The Kuhn-Lloyd question: does the chromatic fixed-point loss of a p-group equal the shortest cyclic subnormal chain length?

Theorem 1.1: for every prime $p$ , finite $p$ -group $G$ , subgroup $H$ and $n\ge0$ , $r_n(G,H)=\ell(G,H)$ , the shortest cyclic subnormal chain length; sharpness is witnessed by finite spectra, and the case $n=0$ includes rational detection. Combined with Balmer-Sanders reductions, a corollary determines the finite-height prime inclusions in the Balmer spectrum of finite genuine $G$ -spectra for every finite group $G$ . Not shown: anything about infinite height beyond what Balmer-Sanders already give, or non-finite spectra.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Kuhn-Lloyd question: does the chromatic fixed-point loss of a p-group equal the shortest cyclic subnormal chain length? · Kuhn-Lloyd chromatic fixed-point loss equality

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No independent mathematician has checked this yet. Checked here: the abstract, introduction and Theorem 1.1 were read against the Kuhn-Lloyd question as the manuscript quotes it; the theorem states the hoped-for equality for every prime, every finite $p$ -group and every height, hence height independence. The proof (profinite character sources, relative integration, telescopic estimates) was not refereed. No Lean formalization accompanies this manuscript.