The BF blowup simple type and homogeneous type conjecture

Let $X$ be a closed, smooth, oriented $4$-manifold with $b_2^+(X)\geq 2$. The Bauer–Furuta invariant has BF blowup simple type and $X$ is of BF homogeneous type. This conjecture extends the Seiberg–Witten simple type conjecture to Bauer–Furuta invariants; the supplied text does not state whether it has been resolved.