The positive-entropy stable ergodicity conjecture

Let $M$ be a compact manifold, let $m$ denote Lebesgue measure, and let $\operatorname{Diff}^{1}_{m}(M)$ be the space of $C^1$ Lebesgue-measure-preserving diffeomorphisms. A diffeomorphism is stably ergodic if every sufficiently close diffeomorphism in the relevant volume-preserving $C^1$ neighborhood is ergodic. Positive-entropy stable ergodicity conjecture. Generically in $\operatorname{Diff}^{1}_{m}(M)$, if $f$ has positive metric entropy with respect to Lebesgue measure, then $f$ is stably ergodic. The conjecture was originally posed in dimension $3$ and is stated here in arbitrary dimension. It was reported as proved in any dimension, so its status is solved.