The PIA conjecture for minimal log discrepancies

Let $(X, \mathfrak{a})$ be a log pair over an algebraically closed field $k$ of characteristic zero, and let $D$ be a normal Cartier prime divisor on $X$. Let $x \in D$ be a closed point, and suppose that $D$ is not contained in the cosupport of the $\mathbb{R}$-ideal sheaf $\mathfrak{a}$. PIA conjecture. One has

$$\operatorname{mld}_x \bigl( X, \mathfrak{a} \mathcal{O}_X(-D) \bigr) = \operatorname{mld}_x (D, \mathfrak{a} \mathcal{O}_D).$$

This is the precise inversion of adjunction conjecture for minimal log discrepancies. The paper describes it as a fundamental conjecture; the supplied text gives no complete resolution, although it notes known cases for klt pairs.