Kashaev's matrix-valued descendant colored Jones conjecture

Let $K$ be a knot, let $N$ be a strictly positive integer, let $n$ be an integer parameter, and let $\zeta$ be a primitive $N$-th root of unity. Write $\langle K\rangle_{N,n}$ for the R-matrix invariant, and let $1_N$ denote the identity $N\times N$ matrix. Matrix-valued colored Jones conjecture. For all knots $K$, strictly positive integers $N$ and $n$, and primitive $N$-th roots of unity $\zeta$,

$$\langle K\rangle_{N,n}=J^K_{n+1}(\zeta)1_N.$$

For $n=-1$, the source explains that the invariant is already a multiple of the identity and recovers the specialization entering the Volume Conjecture; the conjecture extends this identity to arbitrary $n\in\mathbb Z/N\mathbb Z$.