The volume conjecture for colored HOMFLY polynomials

Let $K$ be a hyperbolic knot, and let $J_N^{(n)}(K;q)$ denote the colored HOMFLY polynomial, or $SU(n)$ invariant, associated with the symmetric representation and evaluated at $q$. Let $\operatorname{Vol}(\mathbb{S}^3\backslash K)$ and $\operatorname{CS}(\mathbb{S}^3\backslash K)$ denote the volume and Chern–Simons invariant of the knot complement. Volume conjecture for $SU(n)$ invariant. For $a=0,1,2,\dots,n-2$ and $s\in\mathbb{Z}$, one has

$$2\pi s\,\lim_{N\to\infty}\frac{\log J_N^{(n)}\left(K;\exp\left(\frac{2s\pi i}{N+a}\right)\right)}{N}=\operatorname{Vol}(\mathbb{S}^3\backslash K)+i\operatorname{CS}(\mathbb{S}^3\backslash K).$$

This is presented as an extension of the classical volume conjecture from colored Jones polynomials to colored HOMFLY polynomials. The source does not state a resolution, so its status remains open.