The extension conjecture for intersection forms of smooth four-manifolds with infinite cyclic fundamental group

Let $M$ be a closed smooth $4$-manifold with fundamental group $\mathbb{Z}$, and consider its intersection form on $\pi_2M$.

Extension conjecture. The intersection form on $\pi_2M$ is extended from the integers.

This conjecture would reduce the realization problem for smooth $4$-manifolds with fundamental group $\mathbb{Z}$ to the simply-connected case. The source presents it as an expected statement; its status is not resolved there.