Niţică–Rodriguez Hertz generic stable ergodicity problem

Let $M$ be a compact manifold with volume measure $m$, and let $\operatorname{Diff}^{1}_{m}(M)$ be the space of volume-preserving $C^1$-diffeomorphisms of $M$. For $f\in\operatorname{Diff}^{1}_{m}(M)$, say that all Lyapunov exponents are zero when every Lyapunov exponent of $f$ vanishes, and say that $f$ is stably non-uniformly hyperbolic when it is robustly non-uniformly hyperbolic. Niţică–Rodriguez Hertz's problem. Generically in $\operatorname{Diff}^{1}_{m}(M)$, either all Lyapunov exponents are zero, or $f$ is stably ergodic and stably non-uniformly hyperbolic. The statement is presented as a problem motivated by work on stable ergodicity outside the partially hyperbolic setting; its resolution is not given in the source.