The homological contractibility conjecture for generic oper structures

Let $G$ be the group under consideration, let $X$ be the curve in the geometric Langlands setting, and let $\sigma$ be an irreducible local system. The space of generic oper structures on $\sigma$ is the fiber of the map from generic oper structures to irreducible local systems.

Generic-oper contractibility conjecture. The space of generic oper structures on a given irreducible local system is homologically contractible.

This conjecture is equivalent in the stated setting to the geometric Langlands conjecture and to connectedness of the fibers of the map from generic oper structures to irreducible local systems. The supplied text does not establish whether the conjecture is resolved.