The X = M conjecture for tensor products of Kirillov–Reshetikhin crystals

Let $B$ be a tensor product of Kirillov--Reshetikhin crystals of type $\mathfrak{g}$. For a classical weight $\lambda$, let $X(B,\lambda;q)$ be the one-dimensional sum over classically highest weight elements and let $M(B,\lambda;q)$ be the fermionic formula over $B$-configurations. $X=M$ conjecture.

$$X(B,\lambda;q)=M(B,\lambda;q).$$

The identity connects statistical-mechanical one-dimensional sums with fermionic rigged-configuration formulas. It is known in many cases, but the statement as given for tensor products of KR crystals in arbitrary type is not resolved by the source.