Hausel–Hitchin mirror conjecture for upward flows

Let $C$ be a smooth projective curve, let $M_{r,d}$ be the moduli space of semistable Higgs bundles on $C$, and let $\mathbb G_m$ act by $\lambda\cdot(E,\phi)=(E,\lambda\phi)$. For a sequence of divisors $\delta=(\delta_0,\ldots,\delta_{r-1})$ on $C$, with $\delta_i$ effective for $i>0$, let $W_\delta^+$ be the Lagrangian upward flow associated with the corresponding very stable fixed Higgs bundle, and let $\Lambda_\delta$ be the hyperholomorphic vector bundle constructed in the source. Hausel–Hitchin mirror conjecture. The structure sheaf of the upward flow is mirror to this hyperholomorphic vector bundle:

$$\mathcal O_{W_\delta^+}\quad\text{is mirror to}\quad\Lambda_\delta.$$

This conjecture proposes a mirror-symmetry correspondence between Lagrangian branes arising from upward flows in the Hitchin system and hyperholomorphic vector bundles; the supplied text does not state whether it has been resolved.