Andersen's asymptotic expansion conjecture for Reshetikhin–Turaev invariants

For an oriented compact three-manifold $X$, let $G$ be a semisimple, simply connected Lie group, and let $\mathcal{Z}_G^{(K)}(X)$ denote the Reshetikhin–Turaev TQFT invariant at level $K$. Let $q_0=0,q_1,\dots,q_n$ be the finitely many distinct values of the Chern–Simons functional on the space of flat $G$-connections on $X$. Andersen's asymptotic expansion conjecture. There exist constants $d_{j,r}\in\mathbb{Q}$ and $b_{j,r}\in\mathbb{C}$ for $r=1,\dots,u_j$ and $j=0,1,\dots,n$, and $a_{j,r}^l\in\mathbb{C}$ for $j=0,1,\dots,n$ and $l=1,2,\dots$, such that, as $K\to\infty$,

$$\mathcal{Z}_G^{(K)}(X)\sim\sum_{j=0}^n e^{2\pi iKq_j}\sum_{r=1}^{u_j}K^{d_{j,r}}b_{j,r}\left(1+\sum_{l=1}^\infty a_{j,r}^lK^{-l}\right).$$

The conjecture describes the large-level asymptotics of quantum invariants as a finite sum of contributions indexed by Chern–Simons values of flat connections. The source states that the displayed expansion is solved explicitly for the $G=\operatorname{SL}(2,\mathbb{C})$ version in the setting under discussion; the general statement for semisimple, simply connected $G$ is not resolved here.