The exact WKB analytic continuation conjecture for strongly GMN spectral curves

Let $\nabla$ be a WKB-regular $\hbar$-flat connection with strongly GMN spectral curve, let $\Psi$ be a WKB formal solution, and let $\cL\Psi$ be its Borel–Laplace dual. Let $\theta$ be an unobstructed angle whose existence is assured by the paper's main theorem. Exact WKB analytic continuation conjecture. If $z\in C\bs D$ is not on the Stokes graph at $\theta$, then $\cL\Psi$ is analytically continuable on $\bR_{>0}\cdot e^{2\pi i\theta}$ and is Laplace transformable in direction $\theta$. If $\cT_1,\ldots,\cT_i,\ldots$ are the Stokes trees at $\theta$ passing through $z$, then the first sheet of the analytic continuation of $\cL\Psi$ is smooth on

$$\bR_{>0}\cdot e^{2\pi i\theta}\bs \bigl\{m(\cT_i,\theta)\cdot e^{2\pi i\theta}\bigr\}_i.$$

This is proposed as a higher-order exact WKB statement: away from the Stokes graph one expects Borel summability, while Stokes trees describe the singularities excluded from the first-sheet continuation. The source supplies no proof or resolution, so the conjecture remains open.