Tempered solution ind-sheaves of holonomic D-modules are real-constructible

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

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

Real-constructibility conjecture. The ind-sheaf $Sol^t(\mathcal{M})$ belongs to $D^b_{\mathbb{R}\text{-c}}(\mathrm{I}[\mathbb{C}_X])$. This is presented as a consequence of the paper's preceding conjecture on weak real-constructibility; the supplied text gives no evidence that it has been resolved.