Maximal-Arthur-parameter conjecture for first occurrence on the theta tower

Let $\pi$ be a representation of $G$ and let $\psi^{\max}(\pi)$ denote its maximal Arthur parameter. Let $d^\pm(\pi,\psi^{\max}(\pi))$ be the corresponding going-up or going-down invariant, and let $m_A^{\pm,\alpha}(\pi)=m_A^\pm(\pi)-n-1$, where $m_A^\pm(\pi)$ is the minimal dimension parameter after which the theta lifts are nonzero and of Arthur type. The maximal-parameter conjecture. If

$$d^\pm(\pi,\psi^{\max}(\pi))>1,$$

then

$$d^\pm(\pi,\psi^{\max}(\pi))=m_A^{\pm,\alpha}(\pi).$$

This predicts that the invariant attached to the maximal Arthur parameter detects the point from which the theta lift is stably of Arthur type. The supplied text presents this as an expectation and gives no resolution status.