Global regularized-period conjecture for Arthur packets

Let $G=G(V)\times G(W)$ over a number field, let $\pi\otimes\pi'$ be an irreducible automorphic representation occurring in $\mathcal{A}_{\rm aut}(G)$, and let $F(\nu)$ denote the canonically extended regularized period integral. Let $(M_A,N_A)$ be the associated global A-parameters, let $d(\pi_v,\pi'_v)$ be the local multiplicity, and let $L(M,N,s)$ be the relevant ratio of L-functions. Global regularized-period conjecture. The restriction of $F(\nu)$ to $\pi\otimes\pi'$ is nonzero if and only if: (1) $(M_A,N_A)$ is relevant; (2) $d(\pi_v,\pi'_v)\ne0$ for every place $v$; and (3) $L(M,N,0)\ne0$. Moreover, if (1) and (3) hold, some globally relevant pure inner form admits an automorphic representation with the same A-parameter on which $F(\nu)$ is nonzero. This extends the tempered global period conjecture to non-tempered automorphic representations, subject to the assumed canonical regularization; the source gives no resolution.