The unitary-dual exhaustion conjecture for closures of Arthur representations

Let $G$ be a classical group over a non-Archimedean local field $F$ of characteristic zero. Denote by $\Pi_u(G)$ the unitary dual, and by $\Pi_{\overline{A}}(G)$ and $\Pi_{\overline{A+,\,u}}(G)$ the closures of the Arthur representations and of the unitary enlarged Arthur representations, respectively.

Unitary-dual exhaustion conjecture.

$$\Pi_{\overline{A}}(G)=\Pi_{\overline{A+,\,u}}(G)=\Pi_u(G).$$

This proposes that every unitary representation of a classical group can be obtained from the indicated Arthur representations by the closure operations. The paper proves equality of the two closure constructions for split symplectic and odd special orthogonal groups and verifies the conjecture in several low-corank cases, but the general assertion remains open.