Hsiang–Kleiner conjecture for nonnegatively curved 4-manifolds

Let $M$ be an orientable closed simply connected nonnegatively curved $4$-manifold with an effective isometric $S^1$-action. Hsiang–Kleiner's conjecture. $M$ is diffeomorphic to either $S^4$, ${\bf CP}^2$, ${\bf CP}^2\# \pm {\bf CP}^2$, or $S^2\times S^2$. The source states that the technique of the paper resolves this conjecture without significant additional effort. Thus the classification is no longer open in the context of the paper.