The bounded birational automorphism representation conjecture for dlt pairs

Let $n$ and $d$ be natural numbers, and let $(X,B)$ be a $d$-dimensional projective dlt pair such that

$$n(K_X+B)\sim 0.$$

Let $\operatorname{Bir}(X,B)$ be the group of $B$-birational automorphisms of $(X,B)$, and let

$$\rho_m:\operatorname{Bir}(X,B)\longrightarrow H^0\bigl(X,m(K_X+B)\bigr)$$

be the natural action by pulling back sections. The bounded birational automorphism representation conjecture. There exist $m,N\in\mathbb N$, depending only on $n$ and $d$, such that the image $\rho_m(\operatorname{Bir}(X,B))$ has cardinality at most $N$.

This conjecture is introduced to relate the preceding index conjectures. The source does not state a resolution status or provide a proof.