The AJ conjecture for the colored Jones polynomial and the A-polynomial

Let $K$ be a knot. Denote by $A_K(l,\alpha)$ its $A$-polynomial, by $A_q(K)(l,\alpha^2)$ the specialization at $q=1$ of the $A_q$-polynomial, and let $\varepsilon$ be the evaluation map at $q=1$. AJ conjecture. For any knot $K$,

$$A_K(l,\alpha)=\varepsilon A_q(K)(l,\alpha^2)$$

up to multiplication by an element of $\mathbb{Q}(\alpha)$. The conjecture relates the recurrence satisfied by the colored Jones polynomial to the $A$-polynomial; it has been verified for examples such as twist knots, but is not established in general.