Stuck–Zimmer's IRS rigidity conjecture for higher-rank lattices

Let $\Gamma$ be a center-free irreducible higher-rank lattice. Stuck–Zimmer's IRS rigidity conjecture. For every ergodic probability-measure-preserving action of $\Gamma$ on a probability space, either the space is essentially finite or the action is essentially free. The source attributes this to Stuck and Zimmer and relates it to coamenable subgroup rigidity; it gives no resolution status.