The contracted-bundle conjecture for 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 a Lyapunov stable aperiodic class of $f$. Assume that $\Lambda$ admits a dominated splitting

$$T_{\Lambda}M=E\oplus F.$$

Contracted-bundle conjecture. The bundle $E$ is contracted.

The paper proves the weaker alternative that either $E$ is contracted or $F$ is expanded, and notes that only one of these bundles is hyperbolic. The conjecture asserts that the first alternative always occurs; the source gives no resolution.