Mercat's conjecture on higher-rank Clifford indices

Let $C$ be a curve of genus $g$, and let $E$ be a semistable vector bundle on $C$ of rank $n$ and degree $d$. Write $\mu(E)=d/n$, and let $\gamma_1$ denote the Clifford index of $C$. Mercat's conjecture.

1. If $\gamma_1+2\leq \mu(E)\leq 2g-4-\gamma_1$, then $h^0(E)\leq \frac{d-\gamma_1 n}{2}+n$.
2. If $1\leq \mu(E)\leq \gamma_1+2$, then $h^0(E)\leq \frac{1}{\gamma_1+1}(d-n)+n$.

These bounds are intended as a higher-rank generalization of the classical Clifford inequality. The source recalls the conjecture as originally proposed by Mercat; many low-genus and low-rank cases are known, but the general statement is not settled.