General quantum modularity conjecture for $b[?]$-invariants

Let $M_3$ be a closed three-manifold, let $G$ be an ADE gauge group, and let $\vec{\underline{b}}$ be a boundary-condition label.

General quantum modularity conjecture. The invariant $\widehat Z^G_{\vec{\underline{b}}}(M_3)$ is closely related to a quantum modular form of some kind.

This conjecture extends the observed relationship between $\widehat Z^G$-invariants, quantum modular forms, false theta functions, mock theta functions, and Witten–Reshetikhin–Turaev invariants. Its precise meaning and general validity remain open.