In this talk, I will present recent work on the structure of wave functions in complex Chern-Simons theory on the complement of a hyperbolic knot. The holomorphic blocks conjecturally possess a hidden integrality structure that guarantees the cancellation of potential singularities in the full non-perturbative wave function at rational points. I will describe several general techniques to determine the wave function in the rational case. Finally, I will illustrate our conjectural statements in the benchmark example of the figure-eight knot, whose wave function shares the features of the ground state for a quantum mirror curve. This talk is based on arXiv:2312.00624.