The inhomogeneous AJ conjecture for the nonabelian A-polynomial factor

Let $K$ be a knot. Let $P_K^0(q,E,Q)$ be the factor of the $A_q$-polynomial corresponding to the inhomogeneous recursive relation, let $A_K(l,\alpha)$ be the $A$-polynomial, let $A'_K(l,\alpha)$ denote its nonabelian factor

$$A'_K(l,\alpha)=\frac{A_K(l,\alpha)}{l-1},$$

and let $\varepsilon$ be evaluation at $q=1$. Inhomogeneous AJ conjecture. One has

$$\varepsilon P_K^0(l,\alpha^2)=A'_K(l,\alpha)$$

up to multiplication by an element of $\mathbb{Q}(\alpha)$. This conjecture proposes that the inhomogeneous recurrence detects the nonabelian representation component encoded by the $A$-polynomial; its general status is open.