Finite Mod_{g,n}-orbits are motivic for g≥3

Show that for genus g≥3, any irreducible representation \rho: \pi_1(Σ_{g,n})\to GL_r(\mathbb{C}) whose conjugacy class has finite orbit under Mod_{g,n} underlies, for any complex structure on Σ_{g,n}, a local system of geometric origin.

Background

This is a non-abelian analogue of arithmetic/motivic characterizations, predicting that finite orbits under mapping class group actions correspond to motivic local systems across all complex structures. It ties the topological dynamics directly to the geometry of Hodge and ℓ-adic realizations.