Irrationality conjecture for the cusp translation parameter of hyperbolic knot representations

Let $K$ be a hyperbolic knot in $S^3$, let $R_0$ be the relevant component of the $SL_2(\mathbb{C})$-representation variety, and let $\mu$ and $\lambda$ denote the meridian and longitude. For an irreducible representation $\rho\in R_0$ such that $\rho(\mu)$ and $\rho(\lambda)$ are parabolic, choose a conjugation in which

$$\rho(\mu)=\pm\begin{bmatrix}1&1\\0&1\end{bmatrix},\qquad \rho(\lambda)=\pm\begin{bmatrix}1&t(\rho)\\0&1\end{bmatrix},$$

where $t(\rho)\in\mathbb{C}$. Irrationality conjecture. One has

$$t(\rho)\notin\mathbb{Q}.$$

The claim concerns the cusp translation parameter associated with a parabolic peripheral representation of a hyperbolic knot. The supplied source does not indicate whether this conjecture has been resolved.