Boundary Emergence and Boundary Inversion A Constraint on Ontological Inference and a Law of System Response at Model Limits

This paper presents two distinct but related results within the Paton System. The Boundary Emergence Theorem establishes that singularities and divergences in formal models indicate limits of descriptive applicability rather than ontological origin. The Boundary Inversion Law defines system behaviour at admissibility limits, showing that boundaries which permit continuation under admissible propagation produce termination or reaction when propagation is forced beyond constraint. Together, these results distinguish between what cannot be inferred and what must occur at model limits. Boundary Emergence constrains inference by preventing ontological claims from model breakdown. Boundary Inversion defines the necessary system response when admissibility is exceeded. Under admissible conditions, systems produce stable, compressed structure at the datum and permit continuation. Under forced conditions, the same boundary no longer stabilises structure and instead produces termination or reactive resolution. The transition between these regimes occurs when propagation exceeds admissibility thresholds. This framework introduces no new physical laws. It provides a structural interpretation of model limits and system response, clarifying the separation between inference constraints and behaviour at boundaries.