Minimal reduction type in classical cases

We prove Yun’s minimal reduction conjecture for all classical groups. More precisely, for any topologically nilpotent regular semisimple element $\gamma$, we show that the associated minimal reduction set ${\mathrm{R}\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}(\gamma )$ 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 ${\mathrm{R}\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}(\gamma )$.