The Hilbert–Kunz multiplicity and F-threshold inequality conjecture

Let $(R,\mathfrak{m},K)$ be a local ring. Let $I\subseteq R$ be an ideal generated by a part of a system of parameters $(f_1,\ldots,f_\ell)$, and set $\overline{R}=R/I$. Let $J$ be an $\mathfrak{m}$-primary ideal, and let $c^J(I)$ denote the associated $F$-threshold. Hilbert–Kunz multiplicity and F-threshold conjecture. One has

$$\operatorname{e}_{HK}(J)\leq \operatorname{e}_{HK}(J\overline{R})\frac{(c^J(I))^{\ell}}{\ell^\ell}.$$

This conjecture relates Hilbert–Kunz multiplicities to $F$-thresholds and would give an upper bound in terms of the $F$-threshold of $I$ with respect to $J$. Its resolution is not specified in the source.