Baseilhac–Benedetti and 1-loop invariant correspondence conjecture

Let $M$ be a cusped hyperbolic $3$-manifold with geometric representation, and let $n$ be odd. Consider the normalized 1-loop invariant $\tau_{M,\lambda}(e^{2\pi i/n})/\tau_{M,\lambda}(1)$ at a root of unity. Baseilhac–Benedetti correspondence conjecture. These normalized invariants agree with the Baseilhac–Benedetti invariants of $M$ and its geometric representation at roots of unity. The source presents this as a proposed matching and does not provide a proof or a resolution status.