Zerbini's single-valued multiple zeta value conjecture for modular graph functions

Let $\Gamma$ be a graph, and let

$$D_{\Gamma}(\tau)=\sum_{k=1-l}^l\,\sum_{m,n\geq 0}d_k^{(m,n)}(\Gamma)\,y^kq^m\overline{q}^n$$

be its modular graph function, with $l$ edges, $q=\exp(2\pi i\tau)$, and $y=\pi\,\operatorname{Im}(\tau)$. Denote by $\mathcal{Z}^{\rm sv}$ the algebra of single-valued multiple zeta values. Zerbini's conjecture. The coefficients $d_k^{(m,n)}(\Gamma)$ belong to $\mathcal{Z}^{\rm sv}$. Explicit computations support this assertion, including cases where higher-depth multiple zeta values occur; the conjecture remains open for arbitrary modular graph functions.