Gang's vanishing conjecture for adjoint Reidemeister torsion

Let $M$ be a compact oriented $3$-manifold with torus boundary, and let $\mathcal{X}(M)$ be the character variety of irreducible representations $\pi_1(M)\to \operatorname{SL}_{2}(\mathbb{C})$. Assume that $\mathcal{X}(M)$ consists of $1$-dimensional components and that the interior of $M$ admits a finite-volume hyperbolic structure. Fix a simple closed curve $\mu\subset\partial M$, let $\mathcal{X}_{\mu}^{c}(M)$ be the preimage of $c\in\mathbb{C}$ under the trace function of $\mu$, and let $\tau_{\mu}(M;\rho)$ denote the adjoint Reidemeister torsion associated to $\mu$ and $\rho:\pi_1(M)\to\operatorname{SL}_{2}(\mathbb{C})$. Gang's vanishing conjecture. For generic $c\in\mathbb{C}$,

$$\sum_{[\rho]\in\mathcal{X}_{\mu}^{c}(M)}\frac{1}{\tau_{\mu}(M;\rho)}=0.$$

This conjecture predicts a vanishing identity for adjoint Reidemeister torsion over the finite fiber of the trace function; the supplied text gives no resolution status.