Li–Zhan polyhedral-covering conjecture for Calabi-Yau fiber spaces

Let $f\colon (X,\Delta)\to S$ be a klt Calabi-Yau fiber space.

Polyhedral-covering conjecture.

1. There exists a polyhedral cone $P_M\subset \operatorname{Eff}(X/S)$ such that

$$\operatorname{PsAut}(X/S,\Delta)\cdot P_M\supset \operatorname{Mov}(X/S).$$

2. There exists a polyhedral cone $P_A\subset \operatorname{Eff}(X/S)$ such that

$$\operatorname{Aut}(X/S,\Delta)\cdot P_A\supset \operatorname{Amp}(X/S).$$

The paper describes this as a more tractable conjecture proposed in earlier work and investigates its relationship with the Morrison–Kawamata cone conjecture. The supplied text gives no resolution status.