The geometric multiplicity formula for the GL6 model

Let $G=\operatorname{GL}_6$ with the model $H=\operatorname{GL}_2\ltimes U$, let $\rho_X=\wedge^3$, and let $\pi$ be an irreducible tempered representation with central character trivial on $Z_{G,H}(F)$. Write $\theta_\pi$ for its Harish–Chandra character and $m_{\mathrm{geom}}(\theta_\pi)$ for the geometric multiplicity defined in the paper. The geometric epsilon-factor conjecture.

$$m_{\mathrm{geom}}(\theta_\pi)=\frac{\epsilon(1/2,\pi,\rho_X)+1}{2}.$$

The source says this is equivalent to the epsilon dichotomy for the two GL models and records a resolved status for this candidate; accordingly it is treated as solved in the database.