Hatayama's structural conjecture for the crystal B^{2,s} of type D_n^{(1)}

Let $B^{2,s}$ be a crystal of type $D_n^{(1)}$, and let $B(k\varpi_2)$ denote the classical crystal of highest weight $k\varpi_2$. Let $D_{B^{2,s}}$ be an energy function on $B^{2,s}$. Hatayama's structural conjecture. If the crystal $B^{2,s}$ exists, then, as a classical crystal, it satisfies

$$B^{2,s}\cong\bigoplus_{k=0}^{s}B(k\varpi_2),$$

it is perfect of level $s$, and its energy function satisfies $D_{B^{2,s}}(b)=k-s$ whenever $b$ belongs to the component $B(k\varpi_2)$. These properties are the specific type $D_n^{(1)}$, node $2$ case of the conjectural structure of Kirillov–Reshetikhin crystals. The paper constructs a combinatorial model and proves uniqueness under the assumed existence and stated properties, but the existence of the affine crystal itself remains open in the source.