  Let $G$ be a reductive group and $X$ a smooth projective curve. We prove
that, for $G$ classical and $\sigma$ an arbitrary $G$-local system on $X$, the
space $\overline{\operatorname{Op}}^{gen}_{G,\sigma}$ of generic extended oper
structures on $\sigma$ is homologically contractible. This contractibility
result is crucial for the proof of the geometric Langlands conjecture.
