Local finiteness conjecture for fundamental groups of klt singularities

Let $(X,D)$ be a klt pair and let $x\in X$ be a singular point, so that $\operatorname{Link}(x\in X)$ denotes the link of the singularity. Local finiteness conjecture. The local fundamental group

$$\pi_1(\operatorname{Link}(x\in X))$$

is finite. This is the local finiteness question for klt singularities. The supplied status evidence indicates that a close relation between the global and local questions was established using local-to-global induction, but it does not itself establish that this conjecture is solved.