Precise inversion of adjunction conjecture for minimal log discrepancies

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

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

This is the precise inversion of adjunction statement studied in the paper; the supplied text does not establish its general resolution status.