Stable 2-systole bounds in positive scalar curvature

We prove that the stable 2-systole is uniformly bounded on the space of Riemannian metrics with scalar curvature at least one for closed spin 2-essential manifolds, which includes $S^2\times S^2$, $S^2\times T^n$, and $\mathbb{C}{\mathbb{P}}^{2n+1}$.