The graph-minor generation conjecture for motivic periods

Let $G$ be a graph of type $(Q,M)$, and let $k$ be a weight bound. Its motivic periods are regularised versions of motivic integrals associated with $G$. A graph minor of $G$ is obtained by graph-minor operations, and the weight of a motivic period is its weight in the relevant period algebra.

Graph-minor generation conjecture. The motivic periods of $G$ of weight at most $k$ lie in the algebra generated by regularised motivic periods of graph minors of $G$ having at most $k+1$ edges.

This conjecture proposes a finiteness and product structure for the motivic periods associated with a graph. It is presented as the organising conjecture for the theory, with no resolution stated in the source.