Plaque expansivity conjecture for partially hyperbolic diffeomorphisms

Let $f$ be a partially hyperbolic, dynamically coherent diffeomorphism. It is plaque expansive if there exists $\varepsilon>0$ such that any two $\varepsilon$-central pseudotrajectories $\\{y_k\\}$ and $\\{z_k\\}$ satisfying

$$\operatorname{dist}(y_k,z_k)<\varepsilon,\qquad k\in\mathbb Z,$$

also satisfy

$$z_0\in W^c_{\varepsilon}(y_0).$$

Plaque expansivity conjecture. Any partially hyperbolic, dynamically coherent diffeomorphism is plaque expansive.

Plaque expansivity is a uniqueness-type property for central pseudotrajectories and is important in the theory of partially hyperbolic systems. The source presents the assertion as a conjecture and gives no resolution status here.