Quantum A-polynomial conjecture for knot series

Let $K\subset S^3$ be a knot, let $\Delta_K(x)$ be its Alexander polynomial, and let $f_K(x,q)$ be the normalized knot series. Let $\widehat{A}$ denote the quantum A-polynomial, acting as a $q$-difference operator in $x$.

Quantum A-polynomial conjecture. For any knot $K\subset S^3$,

$$\widehat{A}f_K(x,q)=0.$$

Furthermore,

$$\lim_{q\to1}f_K(x,q)=\operatorname{s.e.}\left(\frac{1}{\Delta_K(x)}\right),$$

where $\operatorname{s.e.}$ is the average of the expansions of the rational function at $x\to0$ and $x\to\infty$. This supplies a boundary value for the recursion and is intended to determine the series together with the quantum A-polynomial equation.