The resurgence conjecture for sections of the wall-crossing bundle

Let $\Gamma$ be a lattice, let ${\bf T}=\operatorname{Hom}(\Gamma,\mathbb{C}^\ast)$, and let $\mathcal{F}(\sigma)$ be the analytic fiber bundle over $\mathbb{C}\setminus\{0\}$ constructed from analytic stability data $\sigma$. Fix $\gamma\in\Gamma$, and let $\chi_\gamma:{\bf T}\to\mathbb{C}^\ast$ be the corresponding character. Let $s(t)$ be a germ at $t=0$ of an analytic section of $\mathcal{F}(\sigma)$.

Resurgence conjecture. In the canonical formal trivialization, the Taylor series of $\chi_\gamma(s(t))$ is resurgent. The same is true for the Taylor series of $\chi_\gamma(\log(s(t)))$.

This conjecture relates analytic stability data and resurgent series in the parameter $t$; it predicts resurgence for observables obtained from analytic sections and their logarithms.