The closure ordering conjecture for local L-parameters in Arthur packets

Let $G$ be a connected reductive group over a non-Archimedean local field $F$, and assume that a theory of local Arthur packets for $G$ exists as conjectured by Arthur. Let $\psi$ be a local Arthur parameter of $G$, and let $Pi_\psi$ be its local Arthur packet. For a representation $pi e Pi_psi$, let $phi_pi$ be its local $L$-parameter, and write $geq_C$ for the closure ordering on local $L$-parameters.

Closure ordering conjecture. For every $pi e Pi_psi$, one has

$$\phi_pi \geq_C \phi_\psi.$$

This conjecture seeks to describe the relation between the local $L$-parameters occurring in an Arthur packet and the parameter defining the packet. Its status for general reductive groups is open.