Colin–Honda growth-rate conjecture for contact homology

Let $M$ be a closed $3$-manifold with a geometric structure, and let $\xi$ be a universally tight contact structure on $M$. Consider the growth rate of contact homology associated with $\xi$. Colin–Honda's conjecture. If $M$ has spherical geometry, this growth rate is linear. If $M$ has a geometric structure that is neither hyperbolic nor spherical, this growth rate is usually polynomial. Colin and Honda propose this as the expected behavior outside the hyperbolic case, complementing the exponential-growth phenomenon discussed earlier; the supplied source gives no resolution of these assertions.