The asymptotic colored-Jones formula with twisted Reidemeister torsion

Let $K$ be a hyperbolic knot, let $u\ne0$ be small, and let $S(u)$ be the asymptotic function defined by

$$S(u):=(2\pi\sqrt{-1}+u)\lim_{N\to\infty}\frac{\log J_N\bigl(K;\exp((2\pi\sqrt{-1}+u)/N)\bigr)}{N}.$$

Let $\mathbb{T}^{K}_{\mu}(u)$ be the twisted Reidemeister torsion of the representation parametrized by $u$ associated with the meridian $\mu$. Twisted Reidemeister torsion conjecture. For small $u\ne0$,

$$J_N\Bigl(K;\exp\bigl((2\pi\sqrt{-1}+u)/N\bigr)\Bigr)=\frac{\sqrt{-\pi}}{2\sinh(u/2)}\mathbb{T}^{K}_{\mu}(u)^{-1/2}\left(\frac{N}{2\pi\sqrt{-1}+u}\right)^{1/2}\exp\left[\frac{S(u)N}{2\pi\sqrt{-1}+u}\right].$$

This proposes a precise leading asymptotic involving the exponential term determined by $S(u)$ and a prefactor given by twisted Reidemeister torsion. The source does not state a resolution beyond the surrounding conjectural discussion.