HKOTT's perfectness conjecture for Kirillov–Reshetikhin crystals

Let $B^{r,s}$ be the Kirillov–Reshetikhin crystal indexed by a node $r$ and a positive integer $s$, and let

$$c_r=\max\left\{\frac{a_r}{a_r^\vee},a_0^\vee\right\},$$

where the coefficients are defined by $\delta=\sum_{j\in I_{\mathop{\rm af}\nolimits}}a_j\alpha_j$ and $c=\sum_{j\in I_{\mathop{\rm af}\nolimits}}a_j^\vee\alpha_j^\vee$.

HKOTT's perfectness conjecture. The crystal $B^{r,s}$ is perfect if and only if $\frac{s}{c_r}$ is an integer. If $B^{r,s}$ is perfect, its level is $\frac{s}{c_r}$.

Perfectness is important for level-zero crystals because it enables the Kyoto path model and the construction of highest-weight affine crystals from semi-infinite tensor products of Kirillov–Reshetikhin crystals. The conjecture was proved for all nonexceptional types, while the statement in full generality is resolved according to the supplied status evidence.