Theorem 4.1

Theorem 4.1 (Generated-chain theorem). Let $S$ be a legally generated chronological scaffold with current top $t$.

1. Its physical graph and its minimal figure are weakly acyclic.

2. The nodes reachable from $t$, and the states of the minimal figure, are totally ordered by reachability.

3. Conversely, every finite behaviorally reduced labelled rooted reachability-chain port graph, with an optional least unlabelled edgeless state, has an exact legal scaffold presentation at some finite distance.