DCC conjecture for Iitaka volumes of log canonical pairs

Let $d$ and $ba$ be positive integers with $ba<d$, and let $b3\remove [0,1]$ be a DCC set. Define

$$\operatorname{Ivol}_\mathrm{lc}^\Gamma(d,\kappa)=\left\{\operatorname{vol}_\kappa(K_X+B)\mid (X,B)\text{ is projective lc},\ \dim X=d,\ \kappa(K_X+B)=\kappa,\ B\in\Gamma\right\}.$$

DCC of Iitaka volumes. The set $\operatorname{Ivol}_\mathrm{lc}^\Gamma(d,\kappa)$ is a DCC set.

This extends the known DCC theorem for usual volumes, corresponding to $\kappa=d$, from klt pairs to log canonical pairs with lower Iitaka dimension. It is open in general; the paper notes that the relevant arguments depend on good minimal models and boundedness of complements, which are currently available only in limited dimensions.