  Motivated by the Quantum Modularity Conjecture and its arithmetic aspects
related to the Habiro ring of a number field, we define a map from the Kauffman
bracket skein module of an integer homology 3-sphere to the Habiro ring, and
use Witten's conjecture (now a theorem) to show that the image is an
effectively computable module of finite rank that can be used to phrase the
quantum modularity conjecture.
