The intrinsic Palis conjecture for homoclinic classes

Let $M$ be a compact manifold and let $\operatorname{Diff}^1(M)$ be the space of $C^1$-diffeomorphisms. A residual subset is a countable intersection of open dense subsets, and the stable dimension of a hyperbolic periodic point is the dimension of its stable bundle. Intrinsic Palis conjecture. There is a residual subset $\mathcal{R}\subset \operatorname{Diff}^1(M)$ such that, for every $f\in\mathcal{R}$, if a homoclinic class $H(p)$ is not hyperbolic, then there is a periodic point $q\in H(p)$ whose stable dimension differs from that of $p$. This is proposed as an intrinsic version of Palis's conjecture because the periodic point with different stable dimension is required to lie inside the non-hyperbolic homoclinic class; the source gives no resolution.