Equivalence conjecture for regular holonomic microdifferential modules

Let $X$ be the underlying complex manifold, and let $\mathcal{E}_X$ and $\widehat{\mathcal{E}}_X$ denote the two sheaves of microdifferential operators appearing in the paper. Consider their categories of regular holonomic modules. Equivalence conjecture. The category of regular holonomic $\mathcal{E}_X$-modules is equivalent to the category of regular holonomic $\widehat{\mathcal{E}}_X$-modules. The proposition immediately preceding the conjecture gives only a full-subcategory inclusion; the equivalence is posed as an open problem, with the source reducing the issue to behavior along a pure codimension-one locus in a conic Lagrangian support.