Loubaton's characterization of the image of the right adjoint embedding

Let $R\colon \Cat^L_\infty\hookrightarrow \Cat_\infty$ be the embedding of the category of presentable $\infty$-categories and colimit-preserving functors into the category of $\infty$-categories, and let an $\infty$-category be $\omega$-complete when it satisfies the relevant completeness condition described in the paper. Loubaton's conjecture. The image of the embedding

$$R\colon \Cat^L_\infty\hookrightarrow \Cat_\infty$$

consists precisely of the $\infty$-categories that are $\omega$-complete. This would make the necessary criterion established earlier sufficient and identify the example of the universal obstruction to a coinductively complete $\infty$-category lying in the image of $R$; the source provides no resolution of the conjecture.