Index conjecture for terminal Calabi–Yau varieties

For $n\ge1$, let $I_{\mathrm{klt}}(n-1,\Phi_{\mathrm{st}})$ denote the set of indices of klt Calabi–Yau pairs of dimension $n-1$ whose coefficients lie in the set $\Phi_{\mathrm{st}}$ of standard coefficients, and let $I_{\mathrm{term}}(n)$ denote the set of indices of terminal Calabi–Yau varieties of dimension $n$. Index conjecture for terminal Calabi–Yau varieties.

$$I_{\mathrm{klt}}(n-1,\Phi_{\mathrm{st}})=I_{\mathrm{term}}(n).$$

This conjecture proposes an equality between the indices of terminal Calabi–Yau varieties and those of lower-dimensional klt Calabi–Yau pairs with standard coefficients, as part of an inductive approach to the index conjecture. Its resolution is not established by the supplied text.