Ambro–Shokurov ACC conjecture for minimal log discrepancies

Let $\Gamma\subset [0,1]$ be a DCC-set, meaning that every decreasing sequence in $\Gamma$ is eventually constant. For a log pair $(X,\Delta)$, write $\operatorname{mld}(Z,X,\Delta)$ for the minimal log discrepancy along a closed subvariety $Z\subset X$, and write $\operatorname{coeff}(\Delta)$ for the set of coefficients of $\Delta$. For a fixed integer $k$, define

$$\Omega_k:=\left\{\operatorname{mld}(Z,X,\Delta)\middle|\begin{array}{l} \dim X=k,\\ (X,\Delta)\text{ is a log pair},\\ Z\subset X\text{ is a closed subvariety},\\ \operatorname{coeff}(\Delta)\in\Gamma \end{array}\right\}.$$

Ambro–Shokurov's ACC conjecture. The set $\Omega_k$ is an ACC-set: every increasing sequence $\alpha_1\leq\alpha_2\leq\cdots$ in $\Omega_k$ eventually becomes stationary.

This is one of the two conjectures about minimal log discrepancies attributed to Ambro and Shokurov in the source. If these conjectures hold, log-flips terminate by the cited theorem of Shokurov; the source does not state a resolution status.