Stokes wall-crossing conjecture for Hitchin stability conditions

Let $G$ be a semisimple complex Lie group, let $X$ be a Riemann surface, let $\mathcal C$ be the associated $3$-dimensional Calabi--Yau category, and consider the component of its moduli space of stability conditions containing the Hitchin base. Stokes wall-crossing conjecture. The behavior of the Stokes factors and the resurgence phenomenon for the Lax pair of the Hitchin system determine the wall-crossing phenomena on that component. The conjecture proposes a correspondence between analytic asymptotic data of the Hitchin Lax pair and categorical wall crossing. The source states this as an expectation and provides no resolution.