OpenAI · 311-01 · 2026-09-24 · Topology

Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectra

preprints/Stabilizer-Orbits-and-Thick-Tensor-Ideals-of-Dualizable-Kn-Local-Spectra-September-24-2026

Family 311. Chai's invariant-ideal conjecture.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

Proves Chai's invariant-ideal conjecture for Lubin–Tate deformation rings over finite residue fields, at every prime and positive height $n$ . Through the implication of Barthel–Heard–Naumann, this proves the Hovey–Strickland conjecture: dualizable $K (n)$ -local spectra have exactly $n + 2$ thick tensor ideals, and their Balmer spectrum is a chain of $n + 1$ points.

We classify the prime and radical ideals of the Lubin–Tate deformation ring invariant under an open Morava stabilizer subgroup, at every prime and positive height. This proves Chai's invariant-ideal conjecture in the standard finite-residue-field formulation. It also proves the Hovey–Strickland conjecture: the dualizable $K (n)$ -local category has exactly $n + 2$ thick tensor ideals, and its Balmer spectrum is a chain of $n + 1$ points.

Preprint source and Lean scope

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