The DAHA–Jones correspondence for double-torus knots

Let $\boldsymbol{c}$ be a simple closed curve on the genus-two surface $\Sigma_{2,0}$, and let $\overline{P}_n(q_u,x_u,x_d;\boldsymbol{c})$ denote its reduced DAHA invariant. The parameters $x_u,x_d,q_u$ are as in the DAHA construction, and the $n$-colored Jones polynomial is normalized up to framing. DAHA–Jones correspondence. The DAHA invariant $\overline{P}_n(q_u,x_u,x_d;\boldsymbol{c})$ coincides with the $n$-colored Jones polynomial for the double-torus knot $\boldsymbol{c}$ up to framing when $x_u=x_d=q_u$. This proposed correspondence is supported by the relation between the constant-term construction and the Jones polynomial, but the supplied text gives no resolution, so the claim remains open.