X=M=K conjecture for stable one-dimensional sums

Let $\overline{K}^{\diamondsuit}_{L,\lambda}(t)$ and $\overline{M}^{\diamondsuit}_{L,\lambda}(t)$ be the $K$- and fermionic formulas associated with an allowed diagram shape $\diamondsuit$, tensor-product data $L$, and dominant weight $\lambda$. X=M=K conjecture. For every allowed $\diamondsuit$,

$$\overline{K}^{\diamondsuit}_{L,\lambda}(t)=\overline{M}^{\diamondsuit}_{L,\lambda}(t^2).$$

This is the paper’s central large-rank identity, relating the type $A$-based $K$ formula to the fermionic formula; the source gives no resolution status.