Generalized Gan-Gross-Prasad relevance characterizes quotient branching

Let $pi in \mathrm{Irr}(G_{n+1})$ and $pi' in \mathrm{Irr}(G_n)$. A pair $(pi,pi')$ is relevant if there exist multisegments $\mathfrak m,\mathfrak n$ such that $(\mathfrak m,\mathfrak n,nu^{1/2}pi)$ is strongly RdLi-commutative and $D^R_{\mathfrak m}(nu^{1/2}cdotpi)\cong D^L_{\mathfrak n}(pi')$. Generalized Gan-Gross-Prasad relevance conjecture. $\mathrm{Hom}_{G_n}(pi,pi')\neq 0$ if and only if $(pi,pi')$ is a relevant pair. This is intended to characterize the quotient branching law for $\mathrm{GL}_n$ over a $p$-adic field; the source presents it as expected and gives no resolution.