The ideal-adic semi-continuity conjecture for minimal log discrepancies

Let $X$ be a klt variety, let $x \in X$ be a closed point, and let $\mathfrak{m}_x$ denote the maximal ideal corresponding to $x$. Ideal-adic semi-continuity conjecture. For every given $r \in \mathbb{R}_{>0}$, there exists $\ell \in \mathbb{Z}_{\ge 0}$ such that, for any ideal sheaves $\mathfrak{a}$ and $\mathfrak{b}$ on $X$ satisfying

$$\mathfrak{a}+\mathfrak{m}_x^\ell=\mathfrak{b}+\mathfrak{m}_x^\ell,$$

one has

$$\operatorname{mld}_x(X,\mathfrak{a}^r)=\operatorname{mld}_x(X,\mathfrak{b}^r).$$

This conjecture asserts that the minimal log discrepancy at $x$ is determined by a sufficiently high ideal-adic jet. The source attributes it to Mustață and Nakamura and presents it in a paper that gives a counterexample to a related conjectural property; the supplied text does not state that this conjecture itself is resolved.