The ascending chain conjecture for canonical thresholds

For an $n$-dimensional variety $X$ and an integral effective divisor $S$, define

$$\mathcal{T}_{n}^{\textup{can}} \colon = \{\operatorname{ct}(X, S) \mid \dim X = n,\ S \text{ is integral and effective}\}.$$

Canonical-threshold ACC conjecture. The set $\mathcal{T}_{n}^{\textup{can}}$ satisfies the ascending chain condition.

This conjecture is motivated by the role of canonical thresholds in the Sarkisov program and is analogous to ACC conjectures for log canonical thresholds and minimal log discrepancies. The supplied paper's abstract states that the threefold case is proved, so the general $n$-dimensional assertion remains open here.