The stability conjecture for discrete series L-packets

Let $F$ be a non-archimedean local field, let $G$ be a connected reductive $F$-group, and let $\Pi_{\varphi}(G)$ be a discrete series $L$-packet of irreducible smooth representations of $G(F)$. A linear combination of the Harish-Chandra characters of members of the packet is a distribution on $G(F)$; a distribution is stable when it is invariant under stable conjugacy. The stability conjecture for discrete series $L$-packets. Every discrete series $L$-packet is stable, meaning that there exists a linear combination of the Harish-Chandra characters of its members that is a stable distribution. Stability is a central expected property of local Langlands packets and is known in many cases through endoscopic methods, but the source does not establish it in the stated generality.