Ambro–Shokurov lower semicontinuity conjecture for minimal log discrepancies

Let $X$ be a normal $\mathbb Q$-Gorenstein variety and let $\Delta$ be an $\mathbb R$-Weil divisor on $X$ such that $K_X+\Delta$ is $\mathbb R$-Cartier. For each integer $d$, let $X^{(d)}$ denote the locus of points of codimension $d$, and let $\operatorname{mld}_{(X,\Delta)}$ be the minimal-log-discrepancy function on this locus.

Ambro–Shokurov's lower semicontinuity conjecture. For each $d$, the function

$$\operatorname{mld}_{(X,\Delta)}:X^{(d)}\longrightarrow\mathbb R\cup\{-\infty\}$$

is lower semi-continuous.

This is the second minimal-log-discrepancy conjecture attributed to Ambro and Shokurov in the source. Together with the ACC conjecture, it is described as relevant to termination of log-flips; the source does not state a resolution status.