Column-catabolizable image conjecture

Let $R$ be a sequence of rectangles such that $R^t$ is dominant. Let $b_R$ be the map from rigged configurations to tableaux, and let $CCT(\lambda;R)$ denote the set of $R$-column-catabolizable tableaux. Column-catabolizable image conjecture.

$$\operatorname{Im}b_R=CCT(\lambda;R).$$

This conjecture connects the image of the rigged-configuration map with the column version of catabolizability and is presented as the counterpart to the row-catabolizable image conjecture.