Rigid local systems are of geometric origin

Prove that every irreducible rigid complex local system on a smooth projective complex variety X arises from geometry, i.e., is of geometric origin.

Background

This conjecture states that isolated points of the Betti moduli—rigid local systems—should be motivic. It is consistent with known cases (e.g., rank ≤3 SL_r-local systems, and rigid local systems on punctured \mathbb{P}^1 with quasi-unipotent local monodromy), and is supported by deep results of Esnault–Groechenig on integrality and p-curvature nilpotence for cohomologically rigid local systems.