Bonatti–Díaz local heterodimensional-cycle conjecture

Let $M$ be a compact smooth manifold without boundary, and let $\operatorname{Diff}^1(M)$ be the space of $C^1$ diffeomorphisms of $M$. A heterodimensional cycle is a pair of hyperbolic periodic orbits with different indices linked by heteroclinic orbits. For a periodic point $p$ and a nearby diffeomorphism $g$, write $p_g$ for the continuation of $p$. Bonatti–Díaz's conjecture. For any generic $f\in\operatorname{Diff}^1(M)$, if a homoclinic class $H(p)$ is not hyperbolic, then arbitrarily $C^1$-close to $f$, there is a diffeomorphism $g$ that exhibits a heterodimensional cycle associated to $p_g$, where $p_g$ is the continuation of $p$. This is presented as a local version, for homoclinic classes, of the generalized Palis conjecture; the source does not state that it has been resolved.