Conjectured minimal volume for exceptional klt Fano varieties

Let $X_n$ be the well-formed exceptional klt Fano $n$-folds constructed in the paper, with anticanonical volume $\operatorname{vol}(-K_{X_n})$.

Minimal-volume conjecture for exceptional Fano varieties. For every integer $n\geq 2$, $X_n$ has the minimum anticanonical volume among all exceptional klt Fano $n$-folds.

Exceptional klt Fano varieties are bounded in each dimension, so their anticanonical volumes have a positive lower bound. The constructed examples attain the smallest known volumes, but minimality in every dimension remains open.