Oper category conjecture for crystals

Let $M_{\l,\mu,\nu}$ be the set of monodromy-free ${}^L G$-opers on $\mathbb{C}\mathbb{P}^1$ with regular singularities of residues $\l,\mu,\nu$ at $0,1,\infty$, respectively. Define $\psi$ by transport along the shortest path between the corresponding degenerate four-point curves, and define $s:M_{\l,\mu,\nu}\to M_{\mu,\l,\nu}$ by the automorphism $z\mapsto1-z$. Oper category conjecture. These maps make the oper category a coboundary monoidal category, and this category is equivalent to the category of $\fg$-crystals. The source reports that this conjecture is proved in type A.