Theorem 3.8

Theorem 3.8 (Minimal residual figure). Every finite rooted scaffold has a canonical finite behavioral figure $M(\mathcal U)$ whose states are $\mathcal R(\mathcal U)$, whose root is $\mathcal U_{\epsilon}$, and whose port $i$ sends $\mathcal U_p$ to $\mathcal U_{pi}$ when defined. The physical reachable graph maps onto $M(\mathcal U)$ by a surjective functional bisimulation. Two rooted scaffolds are behaviorally equivalent if and only if their minimal figures are isomorphic.