Filtered D-module degeneration to the limit category

Let $\mathcal{X}$ be a smooth QCA stack, and let $\operatorname{L}(\Omega_{\mathcal{X}})_{1/2}$ be the half-twisted limit category associated with its cotangent stack. For a coherent D-module $\mathcal{E}\in\mathrm{D}\text{-}\mathrm{mod}_{\mathrm{coh}}(\mathcal{X})$, a good filtration means an object of the coherent filtered D-module category whose underlying D-module is $\mathcal{E}$; write $\mathrm{gr}$ for its associated graded object. Filtered degeneration conjecture. Every $\mathcal{E}\in\mathrm{D}\text{-}\mathrm{mod}_{\mathrm{coh}}(\mathcal{X})$ admits a good filtration such that

$$\mathrm{gr}(\widetilde{\mathcal{E}})\in\operatorname{L}(\Omega_{\mathcal{X}})_{\frac12}.$$

This expresses the limit category as a classical limit of coherent D-modules. The paper discusses a strategy but does not state a resolution.