Arthur's characterization conjecture for local Arthur packets

Let $G=G(V)$ be the classical group associated to a quadratic space $(V,q_V)$, and let $\psi$ be a local Arthur parameter of $G$. For an endoscopic group $G'$ of $G$ and a local Arthur parameter $\psi'$ of $G'$, write $\eta_{\psi'}$ for a stable distribution on $G'$, and let $\operatorname{Tran}_{G'}^G$ denote endoscopic transfer. Let $S_{\psi}$ and $\mathcal{S}_{\psi}$ be the groups appearing in the endoscopic parametrization, let $\chi_V$ be the character of $Z(\widehat{G})^{\Gamma}$ determined by $V$, and set $\widehat{\mathcal{S}}_{\psi,\chi_V}=\\{\varepsilon\in\widehat{\mathcal{S}}_{\psi}\mid \varepsilon(e_0)=\chi_V(-1)\\}$. Arthur's characterization conjecture. (a) For every endoscopic group $G'$ of $G$ and local Arthur parameter $\psi'$ of $G'$, there exists a unique stable distribution $\eta_{\psi'}$ on $G'$ compatible with twisted endoscopic transfers and products. (b-1) If $s\in S_{\psi}$ gives $(G',\psi')\to(\psi,s)$, then $\operatorname{Tran}_{G'}^G(\eta_{\psi'})$ depends only on the image $x$ of $s$ in $\mathcal{S}_{\psi}$; writing this transfer as $\eta_{\psi,x}$, define distributions $\pi(\psi,\varepsilon)$ for $\varepsilon\in\widehat{\mathcal{S}}_{\psi,\chi_V}$ by

$$\eta_{\psi,x}=e(G)\sum_{\varepsilon\in\widehat{\mathcal{S}}_{\psi,\chi_V}}\varepsilon(s_{\psi}x)\pi(\psi,\varepsilon),$$

where $x$ ranges over $\mathcal{S}_{\psi}$. Each $\pi(\psi,\varepsilon)$ is then a non-negative integral linear combination of characters of irreducible representations. This conjectural characterization is the local Arthur-packet statement for pure inner forms of classical groups and is intended to organize stable distributions and their endoscopic transfers. The candidate is attributed in the source to Arthur's stated theorem/conjecture and its formulation for pure inner forms; the supplied material gives no resolution evidence, so its status remains open.