Existence and compatibility conjecture for type D affine Kirillov–Reshetikhin crystals

Let $B^{r,s}$ be the proposed crystal associated with the Kirillov–Reshetikhin module $W^{r,s}$, and let $\tilde{B}^{r,s}$ be the $D_n^{(1)}$-crystal obtained by adding $0$-arrows to the classical crystals using the automorphisms $\sigma$ and the rule

$$f_{0}=\sigma f_{1}\sigma.$$

Type D affine crystal conjecture. If $B^{r,s}$ exists, then

$$\tilde{B}^{r,s}\simeq B^{r,s}.$$

This asserts that the combinatorially constructed affine crystal realizes the desired Kirillov–Reshetikhin crystal; the paper notes that the construction is conjectural, while the case $r=2$ is proved in a special situation.