Gukov's A-polynomial conjecture from colored Jones asymptotics

Let $K$ be a knot in the three-sphere, and let $A_K(L,M)$ denote its $A$-polynomial. For $a\in\mathbb{C}\setminus\mathbb{Q}$, define

$$l(a):=-\frac{d}{da}\left\{a\lim_{N\to\infty}\frac{\log J_N\left(K;\exp(2\pi a\sqrt{-1}/N)\right)}{N}\right\}.$$

Gukov's conjecture. The pair

$$\left(\exp(l(a)),-\exp(\pi a\sqrt{-1})\right)$$

is a zero of the $A$-polynomial of $K$. This conjecture proposes that the asymptotic colored Jones polynomial parametrizes points on the $A$-polynomial curve, connecting quantum knot invariants with the $SL(2,\mathbb{C})$ character variety. The paper records the conjecture as proposed by Gukov; no resolution is supplied in the given text.