Li's conjecture on normalized-volume minimizers

Let $X$ be a variety of dimension $n$, let $x\in X$ be a closed point, and let $\operatorname{Val}_{X,x}$ denote the set of real valuations on $X$ centered at $x$. For $v\in\operatorname{Val}_{X,x}$, write $\nvol_{X,x}(v)$ for its normalized volume. Assume that $X$ has klt singularities at $x$. Li's normalized-volume minimizer conjecture. There exists a valuation $v^\ast\in\operatorname{Val}_{X,x}$ that minimizes $\nvol_{X,x}$. Furthermore, such a minimizer $v^\ast$ is unique up to scaling and quasimonomial. The existence, uniqueness, and quasimonomiality of normalized-volume minimizers connect valuation theory with K-semistability; the source states the claim as Li's conjecture and presents the paper as proving it, while also giving an example showing that a minimizer need not be divisorial.