Morrison–Totaro cone conjecture for klt log Calabi–Yau pairs

Let $(X,\Delta)$ be a klt log Calabi–Yau pair, meaning that $X$ is smooth projective and $\Delta \in |-K_X|$ is linearly equivalent to $\sum_i a_iD_i$ for effective divisors $D_i$ and constants $0 \leq a_i<1$; the case $\Delta=\emptyset$ is allowed. Write $\operatorname{Aut}(X,\Delta)$ for automorphisms preserving $\Delta$, $\operatorname{PsAut}(X,\Delta)$ for pseudo-automorphisms preserving $\Delta$, and let $\mathrm{Nef}^+(X)$ and $\overline{\mathrm{Mov}}^+(X)$ denote the rational hulls of the nef and closed movable cones. Morrison–Totaro cone conjecture. Both of the following actions admit rational polyhedral fundamental domains: the action of $\operatorname{Aut}(X,\Delta)$ on $\mathrm{Nef}^+(X)$, and the action of $\operatorname{PsAut}(X,\Delta)$ on $\overline{\mathrm{Mov}}^+(X)$. Totaro generalized the Morrison cone conjecture from Calabi–Yau varieties to klt log Calabi–Yau pairs. The source does not specify a resolution status.