Partially compactified Radon transform conjecture

Let $P$ and $P^{\vee}$ be the projective spaces replacing the dual projective spaces in the Radon transform, and let $D(P)_{\boldsymbol\nu}$ and $D_{\boldsymbol\nu}$ be the corresponding twisted differential-operator rings. Partially compactified Radon transform conjecture. The derived category of $D(P)_{\boldsymbol\nu}$-modules on $P$ is equivalent to the derived category of $D_{\boldsymbol\nu}$-modules on $P^{\vee}$:

$$R'\colon\mathcal{D}(P,D(P)_{\boldsymbol\nu})\xrightarrow{\sim}\mathcal{D}(P^{\vee},D_{\boldsymbol\nu}).$$

In the $n=4$ case, the source says that this equivalence is mentioned in the cited reference; the general equivalence remains conjectural in the supplied text.