Logarithmic topological mirror symmetry for stringy intersection cohomology

Let $C$ be a smooth projective curve with $g(C)\geq 2$, let $G$ be a connected semisimple group, and let $G^{\vee}$ be its Langlands dual. Let ${\mathcal L}$ be a line bundle on $C$ with $\deg {\mathcal L}>2g(C)-2$, and let $\mathrm{H}_{G,{\mathcal L}}^\mathrm{ss}$ denote the good moduli space of semistable ${\mathcal L}$-twisted $G$-Higgs bundles. Write $\mathrm{IH}_{\mathrm{st}}^*(\mathrm{H}_{G,{\mathcal L}}^\mathrm{ss})$ for its stringy intersection cohomology. Logarithmic topological mirror symmetry conjecture. There exists a natural isomorphism

$$\mathrm{IH}_{\mathrm{st}}^*(\mathrm{H}_{G,{\mathcal L}}^\mathrm{ss}) \cong \mathrm{IH}_{\mathrm{st}}^*(\mathrm{H}_{G^{\vee},{\mathcal L}}^\mathrm{ss}).$$

This is the logarithmic, or $K_C(D)$-twisted for $D>0$, version of topological mirror symmetry; the supplied text does not state its resolution status.