The strengthened local epsilon-factor conjecture for metaplectic representations

Let $F$ be a local field of characteristic $0$, let $\mathbb{M}$ denote the relevant metaplectic group, and let $c_\pi$ be the proportionality constant between the two local functionals defined in the paper. A representation is called good when it satisfies the goodness condition established before the local conjecture. The strengthened local epsilon-factor conjecture. Every representation $\pi\in\operatorname{Irr}_{\operatorname{gen},\operatorname{meta}}\mathbb{M}$ is good and satisfies

$$c_\pi=\epsilon\left(\frac12,\pi,\psi\right).$$

This is presented as a stronger version of the preceding local conjecture and would imply the global identity through the local-to-global theorem. The supplied text records the unramified case of the preceding conjecture but gives no resolution of this stronger assertion.