Ishii's bounded jet-level conjecture for minimal log discrepancies

Let $n\in\mathbb N$, let $I\subset(x_1,\dots,x_{n+c})$ define the $n$-dimensional variety $X=\operatorname{Spec}k[x_1,\dots,x_{n+c}]/I$, and let $s_m(0;X)$ be the jet-scheme invariant defined in the source. Put $0$ for the origin of $\operatorname{Spec}k[x_1,\dots,x_{n+c}]$. Ishii's bounded jet-level conjecture. There exists $N_n\in\mathbb N$, depending only on $n$, such that for every such $X$ there is an $m\leq N_n$ for which either

$$s_m(0;X)=\mathrm{mld}(0;\operatorname{Spec}k[x_1,\dots,x_{n+c}],I^c)\geq 0,$$

or

$$s_m(0;X)<0$$

when $\mathrm{mld}(0;\operatorname{Spec}k[x_1,\dots,x_{n+c}],I^c)=-\infty$. This is one of the conjectures attributed to Ishii in the source; no resolution is given in the supplied text.