Structural properties conjecture for type D Kirillov–Reshetikhin crystals

Let $B^{r,s}$ be a crystal of type $D_n^{(1)}$. Let $B(\Lambda)$ denote the classical $D_n$-crystal of highest weight $\Lambda$, and let the complement of a partition $\Lambda$ in an $r\times s$ rectangle be tiled by vertical dominos. Structural properties conjecture. If $B^{r,s}$ exists, then, as a classical crystal,

$$B^{r,s}\cong\bigoplus_{\Lambda}B(\Lambda),$$

where the sum ranges over exactly those partitions; moreover, $B^{r,s}$ is perfect of level $s$, and it has an energy function $D_{B^{r,s}}$ satisfying $D_{B^{r,s}}(b)=k-s$ whenever $b$ lies in a component $B(\Lambda)$ for which $\Lambda$ differs from the $r\times s$ rectangle by $k$ vertical dominos. The decomposition assertion was subsequently confirmed for the relevant untwisted and twisted cases, whereas the full package is presented as conjectural here.