Shokurov's finite generation conjecture for weak log Fano contractions

Let $(Y/T,B)$ be a weak log Fano contraction, in particular Klt, and let $\{\mathcal{D}_i\}_{i=1}^{\infty}$ be a system of b-divisors. Assume that $\{\mathcal{D}_i\}$ satisfies the following conditions: $\!_{*}\mathcal{O}_Y(i\mathcal{D}_i)$ is a coherent sheaf on $T$ for every $i$; it is log canonically asymptotically saturated; and it is convex, meaning

$$i\mathcal{D}_i+j\mathcal{D}_j\leq (i+j)\mathcal{D}_{i+j}$$

for all $i,j$. FGA conjecture. The system $\{\mathcal{D}_i\}_{i=1}^{\infty}$ stabilises.