Allais' spectral selector conjecture for orderable contact manifolds

Let $(M,\xi)$ be a closed orderable contact manifold, meaning that it admits no positive contractible loop of contactomorphisms. Let $\alpha$ be any contact form supporting $\xi$, and let $c_+^\alpha$ be the associated map from the universal cover of the identity component of the contactomorphism group to $\mathbb{R}$. A map is an $\alpha$-spectral selector when it has the spectrality property associated with the $\alpha$-Reeb dynamics. Allais' spectral selector conjecture. If $(M,\xi)$ is a closed orderable contact manifold, then $c_+^\alpha$ is an $\alpha$-spectral selector for every contact form $\alpha$ supporting $\xi$. This conjecture would supply the missing spectrality property for the contact capacity construction; the cited work establishes other selector properties, but spectrality remains open.