Arone's twisted Koszul self-duality conjecture for orthogonal epimorphisms

Let $\mathsf{OEpi}$ be the category of orthogonal epimorphisms, and let $K(\mathsf{OEpi})$ be its Koszul dual. The mapping spectra between the Weiss derivative functors form a category of sections of the bundles described in the surrounding construction.

Arone's conjecture. The category formed by these sections is equivalent to $K(\mathsf{OEpi})$. Moreover, $\mathsf{OEpi}$ is a twisted Koszul self-dual category: $K(\mathsf{OEpi})$ can be realized by applying the Thom spectrum functor to a category enriched over stable spherical fibrations whose parametrized mapping spectra lie over the mapping spaces of $\mathsf{OEpi}$.

This conjecture concerns the categorical model for the Koszul dual of orthogonal epimorphisms and the resulting twisted self-duality. The paper states it as expected future work rather than proving the equivalence.