Finite-presentation theorem for the tame-diagram subgroup

Let $G(\Gamma)$ be the group associated with the LOT $\Gamma$, let $V(\Gamma)$ be its vertex set, and let $B$ be the subgroup generated by the alternating words in $V(\Gamma)$. A Dehn diagram is tame when its induced track on the disk consists of concentric circles together with arcs joining adjacent track points on the boundary; equivalently, its induced flow has one interior singular point, a sink or a source. Tame-diagram presentation theorem. The group $B$ has a finite presentation whose defining relators are the boundary labels of tame Dehn diagrams. The statement is given in a conjecture environment by the parser, but its wording asserts a theorem; the source context provides no contrary status evidence.