Affine realization conjecture for the spin KR crystal in type D

Let $\mathfrak{g}$ be of type $D_{n+1}^{(1)}$, and let $\widetilde{B}^{n,s}$ be the affine crystal constructed by the stated classical decomposition and affine operators. Spin-crystal realization conjecture. There is an affine-crystal isomorphism

$$\widetilde{B}^{n,s}\cong B^{n,s}\otimes B^{n+1,s}.$$

The paper explains that this conjecture is equivalent to the virtualization conjecture for $B^{n,s}$ of type $A_{2n-1}^{(2)}$; it remains open in the generality stated.