Zero-Plane Rigidity for Einstein Four-Manifolds

We prove that a closed Einstein four-manifold with positive Einstein constant, nonnegative sectional curvature, and a zero-curvature plane has universal Riemannian cover isometric to a product of two round two-spheres. Under the normalization $\mathrm{Ric}=3g$, both spheres have radius $1/\sqrt{3}$. The proof extends coupled estimates for the two Weyl curvature blocks to the boundary of the sectional-curvature cone and determines their equality case.