A-polynomial and defining-curve specialization conjecture

Let $K$ be a knot with complement $M=S^3\setminus K$. Let $\widehat A_M(S_x,x,q^m,q)$ and $\widehat B_M(S_m,q^m,x,q)$ be the content-free, lowest-degree polynomials in the $q$-holonomic ideal that annihilate the descendant state-integrals, and let $S$ be the affine curve defined by the state-integral critical-point equation.

A-polynomial and defining-curve specialization conjecture.

$$\widehat A_M(S_x,x,1,q)$$

is the homogeneous $\widehat A$-polynomial of $K$, and $\widehat A_M(S_x,x,1,1)$ is the $A$-polynomial with meridian variable $x^2$ and longitude variable $S_x$; moreover,

$$\widehat B_M(y,x,1,1)$$

is the defining polynomial of $S$.

These specializations connect the refined $q$-holonomic annihilators of descendant state-integrals to classical knot invariants and the character-curve geometry. The supplied text gives no resolution status.