Scalarity conjecture for the finite-dimensional Yetter–Drinfeld knot invariant

Assume that $q$ is not a root of unity, that $(q,t_1,t_2)$ satisfies $t_1t_2q^n=1$ for some integer $n\geq 1$, and that $(1-t_1)(1-t_2)\ne 0$. Let $Y_n$ be the $4n$-dimensional right Yetter–Drinfeld f-module generated by $v_{n,\alpha}$, and let $T_n$ be the associated $R$-matrix. For a knot $K$, write $J_{T_n}(K)\in\operatorname{End}(Y_n)$ for the resulting knot invariant, and let $V_{n,K}(t,q)$ be its $(1,1)$-entry. Scalarity conjecture. For every knot $K$, we have

$$J_{T_n}(K)=V_{n,K}(t,q)\operatorname{id}_{Y_n}.$$

This claims that the endomorphism-valued invariant associated with the finite-dimensional module is scalar and hence completely determined by its first matrix entry. The supplied text gives no evidence that the claim has been proved or refuted.