The no-splitting conjecture for bi-Lyapunov stable aperiodic classes

Let $M$ be a compact manifold, let $f\in\operatorname{Diff}^1(M)$ be $C^1$-generic, and let $\Lambda$ be an aperiodic class of $f$ that is Lyapunov stable both for $f$ and for $f^{-1}$.

No-splitting conjecture. The class $\Lambda$ admits no non-trivial dominated splitting.

The source says this is a second conjecture and that it would follow from the contracted-bundle conjecture above. It is also known for the bi-Lyapunov stable aperiodic examples constructed in the cited work, but remains open in general.