Complexified volume conjecture for hyperbolic knots and links

Let $K$ be a hyperbolic knot or link, so that $S^3\setminus K$ admits a hyperbolic structure. Let $J_{N-1}(K)$ be the normalized colored Jones polynomial at $q=\exp(\pi i/N)$, and let $\mathrm{Vol}(K)$ denote the hyperbolic volume of $S^3\setminus K$. Let $\mathrm{CS}(K)$ be $2\pi^2$ times the Chern–Simons invariant $cs(S^3\setminus K)$, where $cs(S^3\setminus K)$ is a real number between $0$ and $1/2$. Complexified volume conjecture. For a hyperbolic knot or link $K$,

$$2\,\pi\,\lim_{N\to\infty}\frac{\log J_{N-1}(K)}{N}=\mathrm{Vol}(K)+\mathrm{CS}(K)\,\sqrt{-1}\quad (\operatorname{mod}\ \pi^2\sqrt{-1}\,\mathbb{Z}).$$

This refines the ordinary volume conjecture by incorporating the Chern–Simons invariant into a complex asymptotic. The supplied text does not state whether this conjecture has been resolved.