Virtualization compatibility conjecture for the rigged-configuration bijection

Let

$$B=\bigotimes_{i=1}^N B^{r_i,s_i}$$

be a tensor product of KR crystals, with virtualization map $v$ to the corresponding virtual crystal, and let $\Phi$ be the rigged-configuration bijection. Virtualization compatibility conjecture. The virtualization map $v$ commutes with $\Phi$. This compatibility would show that the bijection is preserved under folding from the virtual simply-laced type.