Finite-generation conjecture for normalized-volume minimizers

Let $x\in (X=\operatorname{Spec}(R),D)$ be a klt singularity, and let $v$ be a minimizer of the normalized-volume function at $x$. Finite-generation conjecture. The associated graded ring

$$\operatorname{gr}_v(R)$$

is finitely generated. This is identified in the paper as the other still-missing part of the stable degeneration conjecture.