Zwegers's radial smoothness and asymptotic matching conjecture for mock theta functions

Let $f$ be a mock theta function in Ramanujan's sense, and let $\xi$ be a root of unity. Radial limits are taken along the line through $\xi$, either inside or outside the unit circle. Zwegers's conjecture. If $\xi$ is a root of unity where $f$ is bounded as $q\to \xi$ radially inside the unit circle, for example $\xi=1$, then $f$ is $C^\infty$ over the line radially through $\xi$. If $\xi$ is a root of unity where $f$ is not bounded, for example $\xi=-1$, then the asymptotic expansion of the bounded term in condition (2) in the definition of a mock theta function is the same as the asymptotic expansion of $f$ as $q\to \xi$ radially outside the unit circle. This conjecture proposes a precise relation between the radial behavior of mock theta functions at roots of unity and the bounded comparison theta-functions in Ramanujan's definition.