The unitary induction conjecture for Dirac cohomology

Let $\pi$ be a unitary representation. A representation is induced by parabolic induction when it is obtained from a representation of a parabolic subgroup in this way. Unitary Dirac-cohomology induction conjecture. A unitary representation either has nonzero Dirac cohomology or is induced from a unitary representation with nonzero Dirac cohomology by parabolic induction. In equal rank, the analogous statement for irreducible tempered representations is recalled in the source with elliptic representations; the stated unitary generalization remains open.