Affine boundedness conjecture for log Calabi–Yau pairs of birational complexity zero

For a positive integer $n$, let $\mathcal{F}_n$ be the family of $n$-dimensional projective varieties $X$ such that there exists a log Calabi--Yau pair $(X,B)$ with

$$K_X+B\sim 0$$

and $c_{\rm bir}(X,B)=0$. Affine boundedness conjecture. The family $\mathcal{F}_n$ is affinely bounded: there exist a scheme $T$ of finite type over the ground field $\mathbb{K}$ and a finite-type affine morphism $\mathcal{U}\to T$ such that every $X\in\mathcal{F}_n$ contains an open affine subset isomorphic to some fiber $\mathcal{U}_t$. The conjecture generalizes the theorem established in dimension two, asserting affine boundedness for surfaces with such log Calabi--Yau structures. Its status in higher dimensions is left open by the source.