Proposition 5.2

Proposition 5.2 (Support captures). The only mixed branches without a strict horizontal residual are $$A/GL(0),\qquad T/GL(0),\qquad T/GL(-1).$$ They require no new generator: the garbage-first path returns along the inverse garbage edge and then takes the original reduction, so $G;G^{-1};R=R$ by vertical cancellation.