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