Contact-order distance conjecture for colored graph representations

Let $G$ be a graph whose vertices are colored with $z$ and $w$, and let $i$ be a vertex from which the representation is computed. The contact order is the order describing how the associated level curves approach one another near a boundary singularity. Contact-order distance conjecture. The contact order of the representation computed from vertex $i$ is twice the path distance from $i$ to the closest vertex colored $w$. The source reports computational evidence for this extension, but does not state a proof or resolution.