The single-valuedness conjecture for two-dimensional completed primitive periods

Let $\Gamma$ be a two-dimensional completed primitive graph, and let $P(\Gamma)$ denote its period. Let ${\mathcal H}^{\mathrm{sv}}$ denote the algebra of single-valued multiple zeta values.

Single-valued period conjecture. The period of any two-dimensional completed primitive graph belongs to

$$P(\Gamma)\in {\mathcal H}^{\mathrm{sv}}.$$

The source presents this as a consequence of the graphical-function single-valuedness conjecture together with a stability theorem. It concerns the arithmetic nature of periods obtained from completed primitive graphs.