Structural Emergence Limits

Systems originate when configuration space first contains an admissible structure capable of sustaining recursive continuation. Previous work within the Paton System identified the admissibility threshold at which minimal configurations become compatible with governing constraints and examined the geometric structure of configuration space regions where such admissible configurations exist. This paper examines the limits of structural emergence. It shows that system formation is constrained not only by the presence of admissible regions within configuration space but also by the boundaries imposed by governing constraints. Many configurations that appear capable of producing systems cannot do so because they violate persistence conditions required for recursive continuation. Structural emergence therefore has limits. Only configurations that both enter an admissible region and remain compatible with governing constraints can produce persistent systems. This framework provides a unified structural explanation for the limits of emergence across physics, biology, computation, and organisational systems.