Primary stranded-graph bound for traceless Hermitian matrix models

Let $\mathcal G$ be a connected vacuum Feynman graph, let $\alpha(\mathcal G)$ denote its large-$D$ exponent, and let $P_{\mathcal G}$ be the associated polynomial. Write $\operatorname{val}P_{\mathcal G}$ for the valuation of this polynomial. Primary stranded-graph bound. One has

$$\alpha(\mathcal G)\leq \operatorname{val}P_{\mathcal G}.$$

The bound is proposed as a graph-by-graph control of the cancellations induced by tracelessness and is intended to support the finiteness and linear growth of $\eta(h)$. Its general validity is not established in the supplied text.