Andersen's topological interpretation conjecture for asymptotic exponents

Let $X$ be a closed oriented $3$-manifold and let $G=\operatorname{SU}(2)$. Let $\mathcal M_j$ be the union of the connected components of the moduli space of flat $G$-connections on $X$ on which the Chern--Simons functional has value $q_j$. For a flat connection $A$, let $h_A^i$ denote the dimension of the $i$th cohomology group of the covariant derivative complex associated with $A$. Andersen's topological interpretation conjecture.

$$D_j=\frac12\max_{A\in\mathcal M_j}(h_A^1-h_A^0),$$

where the maximum means the maximum value of $h_A^1-h_A^0$ on a Zariski open subset of $\mathcal M_j$. The conjecture proposes a topological interpretation of the exponents in the asymptotic expansion: they should be determined by the generic cohomological dimensions of the corresponding Chern--Simons strata. Its status is not resolved in the supplied source.