The Three Fibers Conjecture for Seifert fibered homology spheres

A Seifert fibered homology sphere is a Seifert fibered $3$-manifold that is an integral homology sphere. A homology ball is a smooth $4$-manifold with the same integral homology as the $4$-ball.

Three Fibers Conjecture. A Seifert fibered homology sphere with more than three singular fibers cannot bound a homology ball.

This conjecture concerns the unresolved classification of Seifert fibered homology spheres that bound smooth homology balls. It was first indicated by Fintushel and Stern and explicitly stated by Kollár; the supplied source does not indicate that it has been resolved.