Local finiteness conjecture for slopes of holonomic D-modules

Let $X$ be a complex variety, let $\mathcal{M}$ be a holonomic $\mathcal{D}$-module on $X$, and let $S(\mathcal{M})$ be the union, over germs of hypersurfaces $Z$ of $X$, of the sets $S_Z(\mathcal{M})$ of slopes of $\mathcal{M}$ along $Z$. By Deligne's theorem, each $S_Z(\mathcal{M})$ is finite. Local finiteness conjecture. The set $S(\mathcal{M})$ is locally finite on $X$. This asserts a boundedness property for the slopes of a holonomic $\mathcal{D}$-module as the hypersurface varies; the supplied text gives no resolution status beyond presenting the statement as a conjecture.