Twisted local relative trace formula geometric expansion

Let $\tilde{\mathbf G}$ be the twisted group in the Shalika-period setting, let $\omega$ be the specified central character, and let $\mathcal{C}(\tilde{G},\omega)$ be the strongly cuspidal function space. For a strongly cuspidal $\tilde f$, let $J(\tilde f)$ be the twisted relative distribution and let $J_\mathrm{geom}(\tilde f)=\varepsilon_\mathrm{geom}(\Theta_{\tilde f},\chi)$. Twisted geometric expansion conjecture. For every strongly cuspidal function $\tilde f\in\mathcal{C}(\tilde G,\omega)$,

$$J(\tilde f)=J_\mathrm{geom}(\tilde f).$$

Here $\Theta_{\tilde f}$ denotes the non-invariant weighted orbital integral of $\tilde f$; the supplied text gives no resolution status.