Ducat's conjecture on toric models of rational log Calabi–Yau threefolds

Let $(X,B)$ be a log canonical log Calabi–Yau pair, meaning that $K_X+B$ is numerically trivial, such that $\dim X=3$, $\operatorname{coreg}(X,D)=0$, and $X$ is rational. Ducat's conjecture. Then $(X,D)$ has a toric model. This conjecture concerns the birational classification of rational log Calabi–Yau threefolds; the supplied source does not establish whether it has been resolved.