Andersen–Kashaev's equivalence conjecture for the new Teichmüller TQFT model

Let $X$ be a levelled shaped triangulated oriented pseudo 3-manifold, and let $Z_{\hbar}^{\mathrm{new}}(X)$ be the partition function defined from the Boltzmann weights in the proposed model. The referenced theorem states that this quantity admits analytic continuation to a meromorphic function of the complex shapes and is invariant under all shaped $2$–$3$ and $3$–$2$ Pachner moves along balanced edges. Andersen–Kashaev's equivalence conjecture. The proposed model in that theorem is equivalent to the Teichmüller TQFT from Andersen and Kashaev's earlier work. This conjecture asserts equivalence of the new formulation with the established Teichmüller TQFT, following the theorem's invariance and analytic-continuation properties. Its status is not established in the supplied material.