Crystal structure on Coulomb-branch components

Let $\mathcal M(\mu,\lambda)$ be the Coulomb branch and let $\mathcal A$ be its attracting set. Consider the union, over the relevant weights $\mu$, of the sets of irreducible components of $\mathcal A$ having dimension

$$\frac12\mathop{\text{\rm dim}}\nolimits\mathcal M(\mu,\lambda).$$

Let $L(\lambda)$ be the integrable highest-weight representation of highest weight $\lambda$, with its crystal structure. Coulomb-branch crystal conjecture. This union should have a crystal structure isomorphic to the crystal of $L(\lambda)$. The claim extends the interpretation of attracting-set components as Mirković–Vilonen cycles from dominant weights to arbitrary weights, and the supplied text does not state a resolution.