ACC conjecture for a-lc thresholds on smooth threefolds

Let $P\in X$ be the germ of a smooth threefold, and let $\mathfrak{a}$ and $\mathfrak{b}$ be $\mathbf{R}$-ideals on $X$. For a product of $\mathbf{R}$-ideals, membership in $I$ means that all its exponents belong to $I$. Fix a non-negative real number $a$ and a subset $I$ of the positive real numbers which satisfies the DCC. ACC conjecture for $a$-lc thresholds. The set

$$\{t\in\mathbf{R}_{\ge0}\mid P\in X\text{ a smooth threefold},\ \mathfrak{a},\mathfrak{b}\text{ $\mathbf{R}$-ideals},\ \operatorname{mld}_P(X,\mathfrak{a}\mathfrak{b}^t)=a,\ \mathfrak{a}\mathfrak{b}\in I\}$$

satisfies the ACC. This is presented as a generalisation of the ACC for log canonical thresholds and as one of the conjectures equivalent to the minimal-log-discrepancy ACC conjecture in the paper.