Kottwitz's multiplicity conjecture for global rigid inner forms

Let $G$ be a connected reductive group over a global function field $F$, let $\varphi$ range over the global parameters for $G$, and let $\Pi_\varphi$ be the conjectural global $L$-packet arising from a coherent family of local representations of rigid inner forms. For $\pi\in\Pi_\varphi$, let $\mathcal{S}_\varphi$ be the finite group associated with the centralizer of $\varphi$, let $\langle-,-\rangle\colon\mathcal{S}_\varphi\times\Pi_\varphi\to\mathbb{C}$ be the conjectural pairing, and define

$$m(\varphi,\pi):=|\mathcal{S}_\varphi|^{-1}\sum_{x\in\mathcal{S}_\varphi}\langle x,\pi\rangle.$$

Kottwitz's multiplicity conjecture. The multiplicity of $\pi$ in the discrete spectrum of $G$ is given by

$$\sum_{\varphi}m(\varphi,\pi),$$

where the sum is over all $\varphi$ such that $\pi\in\Pi_\varphi$. This is the proposed global multiplicity formula for coherent rigid inner forms; the source supplies no evidence that it has been proved or refuted.