ASE implies non-uniform sectional expansion

Let $K$ be a partially hyperbolic compact invariant set for a smooth flow. The ASE condition (and, respectively, the $p$ASE condition) is the hypothesis that $K$ has asymptotic sectional expansion (and, respectively, asymptotic $p$-sectional expansion); the NU2SE condition (and, respectively, the NUpSE condition) denotes non-uniform two-sectional expansion (and, respectively, non-uniform $p$-sectional expansion).

ASE-to-NU2SE conjecture. A partially hyperbolic compact invariant set for a smooth flow satisfying the ASE condition (pASE) also satisfies the NU2SE (NUpSE) condition.

The conjecture proposes that asymptotic sectional expansion is sufficient for the corresponding non-uniform sectional expansion, extending the implications known for the weak versions away from trajectories converging to singularities. The source does not state a resolution.