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

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.