The Ran-space oper contractibility conjecture

Let $\operatorname{LocSys}_\cG$ be the stack of $\cG$-local systems and let

$$\operatorname{sv}_{\operatorname{Ran}(X)}:\operatorname{Op}(\cG)^{\operatorname{glob}}_{\operatorname{Ran}(X)}\to\operatorname{LocSys}_\cG$$

be the map from global opers with singularities parametrized by the Ran space. Ran-space oper contractibility conjecture. The fibers of $\operatorname{sv}_{\operatorname{Ran}(X)}$ are $\mathcal O$-contractible; equivalently,

$$\operatorname{sv}_{\operatorname{Ran}(X)}^*:\operatorname{QCoh}(\operatorname{LocSys}_\cG)\to\operatorname{QCoh}(\operatorname{Op}(\cG)^{\operatorname{glob}}_{\operatorname{Ran}(X)})$$

is fully faithful. The source says this is a strengthening of the oper generation conjecture and a theorem for $G=GL_n$, with evidence for classical groups.