Exact WKB convergence conjecture for opers

Let $C$) be a Riemann surface with a compatible $\mathbb{CP}^1$-structure and a spin structure. Let $u=(u_2,\ldots,u_n)\in\bigoplus_{i=2}^n \mathrm{H}^0(C,K^{\otimes i})$, let $W_u^\theta$ be the associated spectral network with angle $\theta$, and let $D_{h.u}$ be the corresponding oper. Let $\Sigma$ be its spectral curve, let $\lambda$ be the Liouville form on $\Sigma$, and let $\mathcal{X}^\theta_\gamma(h)\in\mathbb{C}^*$ denote the holonomy of the abelianized local system for $\gamma\in\mathrm{H}_1(\Sigma)$. Exact WKB convergence conjecture. The exact WKB method in direction $\theta$ applied to the differential equation associated to $D_{h.u}$ converges on the complement of $W_u^\theta$. Moreover, as $h\to0$,

$$\mathcal{X}^\theta_\gamma(h)\sim\exp(Z_\gamma/h),$$

where

$$Z_\gamma=\int_\gamma\lambda\in\mathbb{C}.$$

This conjecture gives a precise convergence statement for exact WKB analysis of higher-order opers and relates the asymptotic holonomies to periods on the spectral curve. The supplied text does not state whether the conjecture has been proved or disproved.