Existence of completely hyperbolic nondegenerate actions on closed manifolds

Let $n\geq 3$ and let $M$ be a closed smooth $n$-dimensional manifold. A completely hyperbolic nondegenerate action of $\mathbb{R}^n$ on $M$ is an action whose orbits and singularities satisfy the completely hyperbolic and nondegenerate conditions defined in the paper.

Existence conjecture. Every closed smooth $n$-dimensional manifold admits a completely hyperbolic nondegenerate action of $\mathbb{R}^n$.

This conjecture proposes that completely hyperbolic nondegenerate actions exist on all closed smooth manifolds in dimensions at least three. The supplied text does not indicate whether the conjecture has been resolved.