Gunningham's conjecture relating instanton Floer homology and generic skein modules

Let $G$ be a reductive group and $M$ a closed, connected, oriented $3$-manifold. Let $\Loc^{\ff}_{G}(M)$ be the representation variety of $G$-local systems, let $\varphi^{\#}_{G}(M)$ be the pullback of the Donaldson–Thomas sheaf to this representation variety, and let $\operatorname{Sk}^{\operatorname{gen}}_{G}(M)$ be the skein module with generic quantum parameters associated to $M$. Gunningham's conjecture. There is an isomorphism

$$\HH^{0}(\Loc^{\ff}_{G}(M),\varphi^{\#}_{G}(M)) \otimes_{\mathbb{C}} \mathbb{C}(q^{1/d}) = \operatorname{Sk}^{\operatorname{gen}}_{G}(M).$$

The conjecture identifies the generic skein module with a scalar extension of the degree-zero cohomology of the framed complexified instanton Floer theory. It is cited in the source as Conjecture D of Gunningham's work.