ACC conjecture for singularity-type sets

Let $a\geq0$ and $d$ be a nonnegative integer. The sets $\mathcal S_d\text{(global)}$, $\mathcal S_d^0\text{(global)}$, $\mathcal S_{a,d}\text{(local)}$, $\overline{\mathcal S}_{a,d}\text{(local)}$, $\mathcal S_{a,d}^0\text{(local)}$, $\overline{\mathcal S}_{a,d}^0\text{(local)}$, $\mathcal S_d$(Mori-Fano), and $\mathcal S_d$(Mori-Fano cn) are the sets of coefficient types defined in the source for the corresponding global, local, Mori–Fano, and canonical Mori–Fano configurations. ACC conjecture for singularity-type sets. Each of these eight sets satisfies the ascending chain condition. This packages several expected ACC statements for coefficient types of pairs and Mori–Fano varieties. The source defines the sets immediately before the assertion and gives no resolution of the combined statement.