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We argue that the description of Feynman loop integrals as integrable systemsis intimately connected with their motivic properties and the action of theCosmic Galois Group. We show how in the case of a family of fishnet graphs,coaction relations between graphs follow directly from iterative constructionsof Q-functions in the Quantum Spectral Curve formalism. Using this observationwe conjecture a "differential equation for numbers" that enter these periods.

Cosmic Wheels: From integrability to the Galois coaction