Asymptotic state-integral conjecture for geometrically nondegenerate representations

Let $K$ be a hyperbolic knot, let $D$ be an open diagram of $K$, and let $\rho$ be a decorated representation of $D$ that is geometrically nondegenerate, meaning that $\rho$ is non-pinched for $D$. For a choice of log-meridian $\mu$, let $\qinv{D,\rho,\mu}$ denote the corresponding quantum invariant, and let $\varsigma_K$ be the normalized $\operatorname{SL}_2(\mathbb{C})$ Chern--Simons invariant of the complete hyperbolic structure. Asymptotic state-integral conjecture. For some choices of $\mu$, there is a constant $\tau$ such that

$$\qinv{D,\rho,\mu}=N^{1/2}e^{N\varsigma_K}\left[\tau+O(N^{-1})\right].$$

This is the proposed saddle-point asymptotic after accounting for the gauge-symmetry directions of the critical manifold. The supplied text presents it as a conjectural conclusion and gives no evidence that it has been proved or disproved.