Strong Palis conjecture for singular flows

Let a flow, equivalently a vector field, be given on a manifold. A singular hyperbolic flow is one whose invariant sets admit the corresponding singular-hyperbolic structure; a homoclinic tangency is a nontransverse homoclinic intersection, and a heterodimensional cycle is a cycle associated with periodic points of different indices. Strong Palis conjecture. In any dimension, every flow (vector field) can be $C^r$-approximated by a singular hyperbolic one or by one displaying a homoclinic tangency or a heterodimensional cycle associated to periodic points. The source presents this as a stronger version of the preceding conjecture and says it was proven in the $C^1$ topology on three-dimensional manifolds, while the general statement remains open in the supplied text.