Garoufalidis's AJ conjecture for knots

Let $K$ be a knot in $S^3$. Its recurrence polynomial is $\alpha_K(t,M,L)$, and let $\varepsilon$ denote specialization at $t=-1$. Let $A_K(M,L)$ be the A-polynomial of $K$.

AJ conjecture. For every knot $K$ in $S^3$, $\varepsilon(\alpha_K)$ is equal to $A_K(M,L)$, up to multiplication by a polynomial depending only on $M$.

The conjecture relates the recurrence polynomial, which encodes a $q$-difference recurrence for the colored Jones polynomial, to the classical A-polynomial. It has been confirmed for the trefoil and figure-eight knots, all torus knots, some two-bridge and pretzel knots, the knot $7_4$, and certain cable knots; the general case remains open.