The maximal-index conjecture for klt Calabi-Yau varieties

Let $n\geq2$, let $X$ be the weighted Calabi-Yau hypersurface constructed in the source, and let $G$ be the cyclic subgroup acting freely in codimension one. Let $m=|G|$. Maximal-index conjecture. The quotient $X/G$ has index $m$, and in every dimension $n\geq2$ this is the largest possible index for a klt Calabi-Yau variety.

The first assertion depends on the conjectured faithfulness of the action on the canonical form; the source reports that the relevant calculation is verified computationally through dimension $30$. The stronger optimality assertion remains without a stated resolution.