Schnetz's cosmic Galois closure conjecture for massless phi-four theory

Let $G$ range over primitive graphs in massless $\phi^4$ theory, and let $I_G^{\mathfrak{m}}$ be their actual motivic amplitudes, meaning amplitudes with trivial numerators. Let $\mathcal{C}_{0,0}$ denote the cosmic Galois group, and let $V$ be the space generated by these amplitudes:

$$V=\operatorname{span}\{I_G^{\mathfrak{m}}:G\text{ is primitive in massless }\phi^4\text{ theory}\}.$$

Schnetz's cosmic Galois closure conjecture. The space $V$ is itself closed under the action of the cosmic Galois group $\mathcal{C}_{0,0}$.

This asserts that cosmic Galois conjugates of primitive massless $\phi^4$ amplitudes remain linear combinations of actual amplitudes of primitive massless $\phi^4$ graphs, rather than requiring generalized amplitudes with arbitrary numerators. The claim is presented as a conjecture and is not resolved in the source.