ACC for generalised epsilon-lc thresholds

Prove the ascending chain condition for generalised $\epsilon$-lc thresholds in arbitrary dimension, beyond the cases currently known, in order to establish termination of the increasing-threshold resolution process for rational maps.

Background

The paper describes a threshold process intended to resolve birational rational maps by repeatedly extracting divisors computing increasing generalised $\epsilon$-lc thresholds. Termination of this process depends on the ascending chain condition for those thresholds.

The authors state that the required ACC is conjectural in general and known in dimension two, while the case $\epsilon=0$ is known in every dimension. Thus the general $\epsilon>0$ case remains unresolved.