Simpson's isosingularity conjecture for filtered local systems and parabolic Higgs bundles

Let $X$ be a compact Riemann surface, let $D\subset X$ be a finite set of marked points, and fix corresponding parameters for filtered local systems and parabolic Higgs bundles of degree zero. Let the two moduli spaces be the semistable moduli space of filtered local systems and the semistable moduli space of parabolic Higgs bundles. Isosingularity conjecture. The Isosingularity theorem holds between these two moduli spaces for fixed corresponding parameters. The analogous étale-isomorphism result is known in the compact, unpunctured case, but remains unknown in the punctured case addressed here.