Remark: Infinite structures

Local finiteness and acyclicity alone do not give a finite ancestral calculation or a well-founded initial-value problem. The chain $\mathbb{Z}$ with edges $j\to j+1$ is locally finite and acyclic but has infinite past at every vertex. The generalization of Theorem thm:order requires a finite ancestral network relative to an input cut, or a separately proved infinite-network construction and convergence theorem.