The Miura-oper description of Iwahori-monodromic critical modules

Let $MOp$ be the scheme of Miura opers with nilpotent singularities, and let $\bD^b(\hg_\crit\operatorname{mod}_\nilp)^{I^0}$ be the Iwahori-monodromic derived category of critical-level modules with nilpotent central support. Miura-oper equivalence conjecture. There exists an equivalence

$$\bD^b(\QCoh( MOp))\simeq \bD^b(\hg_\crit\operatorname{mod}_\nilp)^{I^0}$$

of categories over the scheme $Op$. This conjecture is explicitly attributed to earlier work and is used to describe the Iwahori-monodromic category in terms of quasi-coherent sheaves; the source does not state a resolution.