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Let $X=\overline{X}-D$ be a smooth quasi-projective curve. InarXiv:2110.12300 we constructed a Deligne-Hitchin modui space with Hecke gaugegroupoid for connections of rank $2$. We extend this construction to the caseof any rank $r$, although still keeping a genericity hypothesis. The formalneighborhood of a preferred section corresponding to a tame harmonic bundle isgoverned by a mixed twistor structure.

Twistor space for local systems on an open curve