Colin–Honda exponential-growth conjecture for Reeb orbits

Let $M$ be a closed hyperbolic $3$-manifold with a universally tight contact structure $\xi$, and let $\alpha$ be a non-degenerate contact form defining $\xi$. Denote by $N_L(\alpha)$ the number of Reeb periodic orbits of $\alpha$ with period at most $L$. Colin–Honda's conjecture. The function $N_L(\alpha)$ exhibits exponential growth as $L\to\infty$. This connects the asymptotic abundance of Reeb periodic orbits with the hyperbolic geometry of the underlying manifold; the supplied source gives no resolution of the conjecture.