Geometric multiplicity formula for linear periods

Let $F$ be as in the linear-period setting, let $G=\mathrm{GL}_m(D)$, let $E/F$ be quadratic, let $H$ be the centralizer of $E^\times$ in $G$, and let $m_\mathrm{geom}(\pi,\chi)$ be the geometric multiplicity defined from elliptic-torus orbital integrals. Geometric multiplicity conjecture. For every essentially square-integrable representation $\pi\in\operatorname{Irr}_\mathrm{disc}(G(F))$,

$$m(\pi,\chi)=m_\mathrm{geom}(\pi,\chi).$$

This is attributed in the paper to Wan's conjecture on linear periods; the supplied text does not state that it has been proved or disproved.