Largest anticanonical volume conjecture for Gorenstein terminal Fano varieties

For each odd integer $n\geq5$, let $s_i$ be the sequence used in the paper, and let $X$ be the $n$-fold in the theorem constructing the Gorenstein terminal weighted projective space. Largest-volume conjecture for Gorenstein terminal Fano varieties. The anticanonical volume

$$(-K_X)^n=2^{\frac{n+1}{2}}(s_{\frac{n-1}{2}}-1)^4$$

of $X$ is the largest possible volume among all Gorenstein terminal Fano $n$-folds. The constructed examples have the largest volume among the corresponding Gorenstein terminal weighted projective spaces in the listed odd dimensions, but optimality for all Gorenstein terminal Fano varieties remains open.