The realization conjecture for strong Markovian actions

Let $\rho$ be a strong Markovian action. A strong Markovian action is an action satisfying the strong Markovian-family conditions defined in the source. Realization conjecture for strong Markovian actions. There exists a pseudo-Anosov flow $(M,\Phi)$ such that the action of $\pi_1(M)$ on the bifoliated plane of $\Phi$ is conjugated to $\rho$. The preceding discussion observes that actions associated to pseudo-Anosov flows are strong Markovian, so this conjecture proposes the converse realization of such actions by pseudo-Anosov flows.