Regularity conjecture for tempered solution ind-sheaves

Let $X$ be a complex manifold, let $\mathcal{D}_X$ denote the sheaf of differential operators on $X$, and let $\mathcal{M}$ be a holonomic $\mathcal{D}_X$-module. Write

$$Sol^t(\mathcal{M})=R\mathcal{I}\operatorname{hom}_{\beta_X\mathcal{D}_X}(\beta_X\mathcal{M},\mathcal{O}_X^t).$$

Regularity conjecture. The module $\mathcal{M}$ is regular holonomic if and only if $Sol^t(\mathcal{M})$ is regular. The text notes that the only-if direction follows from the preceding theorem, leaving the converse as the conjectural part; no resolution is supplied.