Demailly–Kollár ascending chain conjecture for log-canonical thresholds

Let $f$ be a holomorphic function germ at the origin in $\mathbb{C}^n$, and let $c_0(f)$ denote its critical integrability index, or log-canonical threshold. Define

$$\mathcal{C}(n)=\{c_0(f):f\in\mathcal{O}_{\mathbb{C}^n,0}\}.$$

Demailly–Kollár's conjecture. The set $\mathcal{C}(n)$ satisfies the ascending chain condition: every ascending sequence in $\mathcal{C}(n)$ eventually stabilizes.

This conjecture concerns the possible log-canonical thresholds of holomorphic function germs and is part of Demailly and Kollár's conjectures on complex singularity exponents. The paper's abstract states that the ascending chain condition is proved, so the conjecture is solved.