Shahidi's strong tempered packet conjecture for quasi-split classical groups

Let $F$ be a local field of characteristic zero, let $G$ be a quasi-split connected reductive $F$-group, and fix a Whittaker datum $\mathfrak{w}$ for $G$. Let $\mathfrak{\phi}$ be a tempered $L$-parameter for $G$, and assume that the corresponding $L$-packet $mathit{Pi}_{\mathfrak{\phi}}$ and its pairing with $\mathcal{S}_{\mathfrak{\phi}}$ have been constructed. Shahidi's strong tempered packet conjecture. Fix a Whittaker datum $\mathfrak{w}$ for $G$. The $L$-packet $mathit{Pi}_{\mathfrak{\phi}}$ contains exactly one $\mathfrak{w}$-generic member $mathit{pi}_{\mathfrak{w}}$, and it satisfies

$$langlecdot,mathit{pi}_{\mathfrak{w}}\rangle_{\mathfrak{\phi}}=\mathbf{1}.$$

This strengthens Shahidi's tempered packet conjecture and concerns the generic member and its character in the packet. The source gives no resolution status.