Adjoint Reidemeister torsion vanishing conjecture

Let $M$ be an oriented compact $3$-manifold with torus boundary, and let $X^\mathrm{irr}(M)$ be the character variety of irreducible $\mathrm{SL}_{2}(\mathbb{C})$-representations. Suppose that every component of $X^\mathrm{irr}(M)$ has dimension $1$ and that the interior of $M$ admits a hyperbolic structure. For a boundary curve $\gamma\subset\partial M$, let $\mathbb{T}_{\gamma}$ denote the adjoint Reidemeister torsion and let

$$\mathrm{tr}_{\gamma}:X^\mathrm{irr}(M)\longrightarrow\mathbb{C}$$

be the trace function of $\gamma$. Adjoint Reidemeister torsion vanishing conjecture. For any boundary curve $\gamma\subset\partial M$ and generic $C\in\mathbb{C}$,

$$\sum_{\chi_\rho\in\mathrm{tr}_{\gamma}^{-1}(C)}\frac{1}{\mathbb{T}_{\gamma}(\chi_\rho)}=0.$$

The paper's abstract states that this conjectural identity is proved for all hyperbolic twist-knot exteriors, while the general claim under the stated hypotheses is presented as conjectural.