The absolute index conjecture for klt Calabi–Yau varieties

Let $d$ be a natural number, and let $X$ be a projective klt Calabi–Yau variety of dimension $d$, meaning that

$$K_X\sim_\mathbb Q0.$$

The absolute index conjecture. There exists a positive integer $n$, depending only on $d$, such that

$$nK_X\sim 0.$$

This is the zero-boundary special case of the index conjecture and is related in the source to minimal log discrepancies near $1$ for Calabi–Yau varieties. The source does not provide a resolution status for this conjecture.