Minimal-volume canonical Calabi–Yau divisor conjecture

Let $s_0=2$ and $s_m=s_{m-1}(s_{m-1}-1)+1$ for $m\geq 1$ be Sylvester's sequence. For a positive integer $n$, let $X$ be the $n$-fold given by the canonical Calabi–Yau hypersurface construction in Proposition 1. Minimal-volume canonical Calabi–Yau divisor conjecture. The ample Weil divisor $\mathcal{O}_X(1)$ has minimal volume among all ample Weil divisors on canonical $n$-folds $X$ satisfying $K_X\sim_{\mathbb{Q}}0$. The conjecture is motivated by exact minimal-volume results for the cited low-dimensional cases, but its assertion in all dimensions remains open.