Bigraded refinement of skein-module Langlands duality

Let $G$ be the group appearing in the skein construction, let $Z$ denote the relevant central subgroup, and let $\pi_1$ denote the corresponding fundamental-group twist. For a closed oriented 3-manifold $M$, write $\mathrm{Sk}_{G,Z}^{a,b}(M)$ and $\mathrm{Sk}_{{^LG},\pi_1}^{b,a}(M)$ for the bigraded skein modules, with the indices exchanged under Langlands duality. Suppose that $q\in\mathbb{C}^\times$ is transcendental. Bigraded refinement conjecture. One has

$$\dim\mathrm{Sk}_{G,Z}^{a,b}(M)=\dim\mathrm{Sk}_{{^LG},\pi_1}^{b,a}(M).$$

This refines the ungraded skein-module duality by keeping track of electric and magnetic one-form-symmetry gradings. Its status is not resolved in the supplied text.