Finite determination conjecture for Mather–Jacobian minimal log discrepancies below a threshold

Let $X$ be a $d$-dimensional variety, let $x\in X$ be a closed point, and let $s_m(X,x)=(m+1)d-\dim X_m(x)$, where $X_m(x)$ is the local $m$-jet scheme at $x$. Let $\delta$ be an integer with $\delta\leq d$. Threshold finite determination conjecture. There exists $N_{d,\delta}\in {\mathbb N}$ depending only on $d$ and $\delta$ such that, whenever $\mathrm{mld_{MJ}}(x;X)<\delta$, there is an $m\leq N_{d,\delta}$ with

$$s_m(X,x)<\delta.$$

These conjectures split the finite determination conjecture into bounds at fixed thresholds; the source presents them as conjectural and states no resolution.