Gunningham–Safronov's derived skein–DT cohomology conjecture

Let $q$ be generic, let $M$ be a connected closed oriented 3-manifold, let $\mathrm{Loc}_G(M)$ be its character stack, and let $\phi_{\mathrm{Loc}_G(M)}$ be its DT sheaf. Let $\mathcal{S}\mathrm{k}_G(M)$ denote the derived skein module and $\mathrm{H}^{\bullet}_{\Delta}$ renormalized cohomology.

Derived skein–DT conjecture. There is an isomorphism

$$\mathrm{H}_\bullet(\mathcal{S}\mathrm{k}_G(M))\cong \mathrm{H}^{-\bullet}_{\Delta}(\mathrm{Loc}_G(M),\phi_{\mathrm{Loc}_G(M)}).$$

This conjecture is the proposed chain-level enhancement of the underived skein–DT comparison, with full derived skein homology recovering renormalized DT-sheaf cohomology. The source mentions partial evidence but does not state a resolution.