Minimal reduction type in classical cases

Abstract: We prove Yun's minimal reduction conjecture for all classical groups. More precisely, for any topologically nilpotent regular semisimple element $γ$, we show that the associated minimal reduction set $\mathrm{RT}{\mathrm{min}}(γ)$ consists of a single nilpotent orbit. This result confirms and extends Yun's earlier work in types A and C, and resolves the remaining cases in types B and D. Moreover, we provide an explicit and effective procedure for determining $\mathrm{RT}{\mathrm{min}}(γ)$.