Gevrey solution conjecture for holonomic \mathscr{D}-modules on the subanalytic site

Let $X$ be a complex manifold, let $\rho_{\rm sa}$ denote the morphism from the subanalytic site of $X$ to $X$, and let $\rho_{\rm sa!}$, $\rho_{\rm sa}^{-1}$, and $\rho_{\rm sa*}$ have their usual meanings. Let $\mathscr{M}$ be a holonomic $\mathscr{D}_X$-module, and let $\mathscr{O}^{\rm gev}_{X_{\rm sa}}$ and $\mathscr{O}^{\rm gev(s)}_{X_{\rm sa}}$ denote the Gevrey-type sheaves occurring in the statement. Then the natural morphism

$${\mathbb R\mathscr{H}om}_{\mathscr{D}_{X_{\rm sa}}}({\rho_{\rm sa}}_!\mathscr{M},\mathscr{O}^{\rm gev}_{X_{\rm sa}})\xrightarrow[]{} {\mathbb R\mathscr{H}om}_{\mathscr{D}_{X_{\rm sa}}}({\rho_{\rm sa}}_!\mathscr{M},\mathscr{O}_{X_{\rm sa}})$$

is an isomorphism, equivalently,

$${\mathbb R\mathscr{H}om}_{\mathscr{D}_{X_{\rm sa}}}({\rho_{\rm sa}}_!\mathscr{M},\mathscr{O}^{\rm gev}_{X_{\rm sa}})\simeq \mathbb R{\rho_{\rm sa}}_*{\mathbb R\mathscr{H}om}_{\mathscr{D}_X}(\mathscr{M},\mathscr{O}_X).$$

Moreover, there exists a discrete set $Z\subset {\mathbb R}_{>1}$ such that the morphisms

$${\mathbb R\mathscr{H}om}_{\mathscr{D}_{X_{\rm sa}}}(\mathscr{M},\mathscr{O}^{\rm gev(s)}_{X_{\rm sa}})\xrightarrow[]{} {\mathbb R\mathscr{H}om}_{\mathscr{D}_{X_{\rm sa}}}(\mathscr{M},\mathscr{O}^{\rm gev(t)}_{X_{\rm sa}})$$

are isomorphisms for $s\leq t$ in the same components of ${\mathbb R}_{>1}\setminus Z$. Gevrey solution conjecture. The stated Gevrey solution comparison and local constancy assertions should hold for every holonomic $\mathscr{D}_X$-module.