The Galois coaction on ${\varphi }^4$ periods

We report on calculations of Feynman periods of primitive log-divergent ${\varphi }^4$ graphs up to eleven loops. The structure of ${\varphi }^4$ periods is described by a series of conjectures. In particular, we discuss the possibility that ${\varphi }^4$ periods are a comodule under the Galois coaction. Finally, we compare the results with the periods of primitive log-divergent non-${\varphi }^4$ graphs up to eight loops and find remarkable differences to ${\varphi }^4$ periods. Explicit results for all periods we could compute are provided in ancillary files.