Spectral invariance conjecture for periods of Reeb orbits

Let $(M,D,g)$ be a three-dimensional contact manifold with sub-Riemannian Laplacian $\Delta_{sR}$ and Reeb flow associated with the canonical contact form determined by $(D,g)$. A period of a Reeb orbit is the time required for the Reeb flow to return to its starting point. Spectral invariance conjecture. The periods of the Reeb orbits are spectral invariants of the sR Laplacian $\Delta_{sR}$.