2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116390We prove new instances of Simpson's rigidity conjecture which states that quasi-unipotent rigid local systems should be motivic. We construct new relative motives over the fourfold punctured Riemann sphere which give rise to $G_2$-rigid local systems which are not rigid in the group $\GL_7.$Algebraic Geometrytext