The non-root-of-unity extension conjecture for skein-module finiteness and holonomicity

Let $q\in\mathbb{C}^\times$ be a quantum parameter, and consider the finiteness and holonomicity assertions for skein modules stated in Theorems and. Non-root-of-unity extension conjecture. The assertions of those theorems hold whenever $q$ is not a root of unity. The paper explains that skein modules of 3-manifolds have substantial $q$-torsion and that the methods developed allow specialization to arbitrary complex values of $q$; proving this conjecture requires controlling the relevant $q$-torsion beyond roots of unity.