Garoufalidis–Yoon twisted 1-loop conjecture

Let $M$ be a cusped hyperbolic 3-manifold, let $\mathcal{T}$ be an ideal triangulation, and choose an epimorphism $\alpha:\pi_1(M)\twoheadrightarrow\mathbb{Z}$, equivalently an infinite cyclic cover, to define the twisted gluing data. Let $\tau^\mathrm{CS}(\mathcal{T},t)$ denote the twisted 1-loop invariant and let $\tau(M,t)$ denote the adjoint twisted Alexander polynomial associated with the geometric representation and $\alpha$. Both are Laurent polynomials in $t$ over the trace field, well-defined up to multiplication by units in $\mathbb{Z}[t^{\pm1}]$. Garoufalidis–Yoon's twisted 1-loop conjecture.

$$\tau^\mathrm{CS}(\mathcal{T},t)=\tau(M,t).$$

This conjecture relates twisted gluing-equation data to the adjoint twisted Alexander polynomial. The paper proves it for all hyperbolic once-punctured torus bundles, so the unrestricted statement is not resolved by the supplied text.