Finite determination conjecture for Mather–Jacobian minimal log discrepancies

Let $X$ be a variety of dimension $d$, let $x$ be a closed point of $X$, and define

$$s_m(X,x)=(m+1)d-\dim X_m(x),$$

where $X_m(x)$ is the local $m$-jet scheme of $X$ at $x$. Finite determination conjecture. For every positive integer $d$, there exists $N_d\in {\mathbb N}$ depending only on $d$ such that, for every closed point $x\in X$ of any $d$-dimensional variety $X$, there exists $m\leq N_d$ satisfying either

$$s_m(X,x)={\mathrm{mld_{MJ}}}(x;X)\geq 0,$$

or

$$s_m(X,x)<0\quad\text{when }{\mathrm{mld_{MJ}}}(x;X)=-\infty.$$

The conjecture would give a uniform finite bound for detecting Mather–Jacobian minimal log discrepancies through local jet schemes; its status is unresolved in the source.