Bertram–Feinberg–Mukai conjecture for rank-two canonical bundles

Set $\rho_{g,k}:=3g-3-\binom{k+1}{2}$. Let $C$ be a general curve of genus $g\geq 2$, and consider the moduli space of stable rank-two vector bundles on $C$ with canonical determinant and $k$ sections. Bertram–Feinberg–Mukai conjecture. This moduli space is non-empty and has expected dimension $\rho_{g,k}$ whenever $\rho_{g,k}\geq 0$; when $\rho_{g,k}<0$, it is empty. This conjecture motivates the study of quadratic Strong Maximal Rank Conjecture loci and connects their geometry with rank-two Brill–Noether theory. The supplied context does not state whether the conjecture has been resolved.