Trisected 11/8-conjecture

Let $X$ be a four-manifold admitting a $(g,0)$-trisection, and suppose its intersection form is even and indefinite. Write $\sigma(X)$ for the signature of $X$.

Trisected 11/8-conjecture. One has

$$g\geq \frac{11}{8}\sigma(X).$$

This is a trisection analogue of the classical $11/8$-conjecture, which predicts $b_2(X)\geq \frac{11}{8}\sigma(X)$ for the relevant smooth, closed, oriented, simply-connected four-manifolds. Its status is open.