Stable ergodicity is open and dense for volume-preserving diffeomorphism tuples

Let $M$ be a compact Riemannian manifold, let $r$ be sufficiently large, and let $m\geq 2$ be an integer. An $m$-tuple of $C^r$ volume-preserving diffeomorphisms of $M$ is called $C^r$-stably ergodic if every sufficiently $C^r$-close $m$-tuple is ergodic with respect to the preserved volume. Stable ergodicity conjecture. $C^r$-stable ergodicity is open and dense among $m$-tuples of $C^r$ volume-preserving diffeomorphisms of $M$. This concerns the genericity of robust ergodicity for volume-preserving iterated function systems; the supplied text gives no resolution status.