Equivalent 11/8-conjecture for the bounding genus and ds-invariant

Let $Y$ be a homology $3$-sphere with $(Y)=0$, and let $\frak{ds}(Y)$ be finite. The bounding genus $|Y|$ is the invariant defined using homologically $1$-connected bounding $4$-manifolds with intersection form $nH$. Equivalent 11/8-conjecture. One should have

$$|Y|\ge \frac{3}{2}\frak{ds}(Y).$$

The source presents this as an equivalent formulation of Matsumoto's $11/8$-conjecture. No resolution status is supplied.