Arinkin's tamely ramified geometric Langlands conjecture for parabolic connections

Let $\mathcal{M}$ be the moduli stack of parabolic connections, let $P$ be the corresponding coarse moduli space of indecomposable quasi-parabolic $\mathfrak{sl}_2$-bundles, and let $D(P)_{\boldsymbol\nu}$ be the twisted differential-operator ring on $P$ determined by the Okamoto map. Write $\mathcal{D}_{qc}(\mathcal{M})^{\pm}$ for the subcategories on which $-1\in\mu_2$ acts on every cohomology sheaf as $\pm1$. Arinkin's tamely ramified geometric Langlands conjecture. The connected component $\mathcal{D}_{qc}(\mathcal{M})^-$ is equivalent to the derived category of $D(P)_{\boldsymbol\nu}$-modules on $P$:

$$L\colon\mathcal{D}_{qc}(\mathcal{M})^-\xrightarrow{\sim}\mathcal{D}(P,D(P)_{\boldsymbol\nu}).$$

This is presented as a conjectural version of the tamely ramified geometric Langlands correspondence in the parabolic setting; its status is not resolved in the supplied text.