Simpson conjectured that for a reductive group $G$, rigid $G$-local systems on a smooth projective complex variety are integral. I will discuss a proof of integrality for cohomologically rigid $G$-local systems. This generalizes and is inspired by work of Esnault and Groechenig for $GL_n$. Surprisingly, the main tools used in the proof (for general $G$ and $GL_n$) are the work of L. Lafforgue on the Langlands program for curves over function fields, and work of Drinfeld on companions of $\ell$-adic sheaves. The major differences between general $G$ and $GL_n$ are first to make sense of companions for $G$-local systems, and second to show that the monodromy group of a rigid G-local system is semisimple. \\ \\ All work is joint with Stefan Patrikis.