Archimedean theta-packet conjecture

Let $F$ be a real or complex local field, let $G$ be an even orthogonal or unitary group over $F$, and let $\psi$ be a local $A$-parameter with bounded image on the Weil group. Let $\Pi_\psi^\theta(G)$ be the theta-packet constructed from local theta correspondence, together with its component-group parametrization. Archimedean theta-packet conjecture. The properties listed for $\Pi_\psi^\theta(G)$ over non-Archimedean fields in the theorem preceding this conjecture also hold when $F$ is real or complex. These properties concern independence from the auxiliary dual-pair choices and auxiliary data, multiplicity-freeness, agreement with Moeglin's packet where defined, containment of the associated $L$-packet, and satisfaction of LIR-B. The conjecture extends the established non-Archimedean description of theta-packets to Archimedean local fields; the source does not state that it has been proved.