Definition: Tree datum

A tree datum consists of a finite vertex set $V=I\bigsqcup X$ with $|X|=n\ge 1$ external and $I$ internal vertices, a tree $T$ on $V$ (connected, $|E(T)|=|V|-1$) with an orientation of each line, a balanced line $k_{\ell }$ for each $\ell =(a,b)\in E(T)$, placed on the variables $(x_a,x_b)$, and a smooth weight $w_a$ for each $a\in V$. The support hypothesis is