The single-valuedness conjecture for two-dimensional graphical functions

Let $\Gamma$ be a graph, and let $f^{(0)}_\Gamma$ denote its two-dimensional graphical function. Let ${\mathcal A}^{\mathrm{sv}}$ be the algebra of single-valued functions defined in the source.

Single-valued graphical-function conjecture. For any graph $\Gamma$,

$$f^{(0)}_\Gamma\in {\mathcal A}^{\mathrm{sv}}.$$

This predicts that two-dimensional graphical functions belong to the single-valued function algebra. The claim is used later to conjecture single-valuedness of periods of completed primitive graphs.