The GM series conjecture for links

Let $L$ be an $l$-component link, let $J_L(n_1,\ldots,n_l;q)$ be its colored Jones polynomials, and let $\nabla_L(x_1,\ldots,x_l)$ be its Alexander–Conway function. The link GM-series conjecture. There is a link invariant $F_L(x_1,\ldots,x_l,q)$, a series in the $x_i$ and $q$ with integer coefficients, such that, near $\hbar=0$ with each $x_i=q^{n_i}=e^{n_i\hbar}$ fixed,

$$F_L(x_1,\ldots,x_l,q=e^\hbar)=\sum_{j\geq0}\frac{P_L(j;x_1,\ldots,x_l)}{\nabla_L(x_1,\ldots,x_l)^{2j+1}}\frac{\hbar^j}{j!}.$$

Moreover, $F_L$ is annihilated by every $q$-difference equation annihilating the colored Jones polynomials of $L$. This extends the knot conjectures experimentally to links; the source supplies examples but no general proof.