The quantum volume conjecture for knots

Let $K\subset S^3$ be a knot, and let $A_K(m,\ell)=0$ be its $A$-polynomial curve. Put $(m,\ell)=(e^u,e^v)$, and let $S_0(u)$ be defined by the wave-function equations in the source. The coloured Jones polynomial has the asymptotic expansion described in the source. Kashaev–Murakami–Murakami–Gukov volume conjecture. For the curve defined by $A_K(m,\ell)=0$, one has

$$S_0(u)=\text{volume of the incomplete hyperbolic manifold }S^3-K.$$

This is a quantum-curve formulation of the volume conjecture relating the asymptotics of the coloured Jones polynomial to hyperbolic volume. The source attributes it to Kashaev, Murakami–Murakami, and Gukov, but gives no resolution status.