The AL-structure characterization conjecture via normally hyperbolic skeleta

Let $(V,\d7\omega,\d7\lambda)$ be a $4$-dimensional finite type Liouville manifold. Its skeleton $\d7\mathfrak{skel}$ is the set used in the source, and the Liouville flow is the flow generated by the Liouville vector field. Assume that

$$\d7\mathfrak{skel}\d7\text{ is a codimension-}1\ \mathcal{C}^1\text{ submanifold},$$

$\d7\mathfrak{skel}$ is normally hyperbolic with respect to the Liouville flow, and the Liouville flow induces an Anosov flow $\d7\Phi$ on $dmathfrak{skel}$. AL-structure characterization conjecture. Then $(V,\d7\omega,\d7\lambda)$ is exact symplectomorphic to an AL structure supporting $dPhi$. The conjecture would characterize AL manifolds from the regularity and dynamical properties of their skeleta; the source does not state that it has been resolved.