The anchor-cell excess conjecture for canonical systems on metric graphs with skeleton K_4

Let $\Gamma$ be a metric graph whose skeleton is the complete graph $K_4$, and let $D=K$ be its canonical divisor. Write $|D|$ for the associated linear system, and call the cells in $|D|$ anchor cells and vertices in $|D|$ vertices. Anchor-cell excess conjecture. The number of anchor cells in $|D|$ minus the number of vertices in $|D|$ is always $16$. This is an observed computational pattern for the listed metrics on $K_4$; whether it holds for every metric on a trivalent graph with skeleton $K_4$ remains to be established.