The orientation-vanishing conjecture for Seiberg–Witten invariants

Let $X$ be a simply connected, closed, oriented, smooth $4$-manifold with $b_2^+(X)>1$ and $b_2^-(X)>1$. Orientation-vanishing conjecture. The Seiberg–Witten invariant vanishes for at least one orientation of $X$. The conjecture concerns the constraint imposed by choosing an orientation; the supplied text gives no resolution status.