Complex-constructible wrapping conjecture

Let $M$ be a compact complex manifold, and let $\Sh_{\mathbb C\text{-}c}(M)$ denote the derived category of $\mathbb C$-constructible sheaves. For a Riemannian metric $g$ on $M$, let $\Phi_t$ be the sheaf quantization of the geodesic flow, with its continuation maps forming an inductive system.

Complex-constructible wrapping conjecture. For every object $\mathcal E$ of $\Sh_{\mathbb C\text{-}c}(M)$, there exists an inductive system $\{\mathcal E_i\}$ in $\Sh_{\mathbb C\text{-}c}(M)$ such that

$$\lim_{t\rightarrow +\infty}\Phi_t(\mathcal E)=\lim_{i\rightarrow +\infty}\mathcal E_i.$$

This asserts that the limiting wrapped object can be represented as a limit of complex-constructible sheaves. The source presents it as a conjectural relationship between ordinary wrapping and complex-constructible objects.