The infinite exotic smooth structures conjecture for simply connected 4-manifolds

Let $X$ be a simply connected smooth $4$-manifold with $b^+\geq 1$.

Infinite exotic smooth structures conjecture. There are infinitely many mutually nondiffeomorphic $4$-manifolds homeomorphic to $X$.

This conjecture concerns the classification of smooth structures within a fixed homeomorphism type, a central problem in smooth $4$-manifold theory. It remains open in the stated generality.