Validating Admissibility Flow: A First Cross-Domain Application of the PFL-X Symbolic Language

This paper presents the first applied validation of the Pressure-Flow Language Extension (PFL-X), a symbolic representation for admissibility-based system behaviour. Rather than proposing new models, the study tests whether PFL-X can consistently describe and align real-world system behaviour across domains. Three domains are examined: artificial intelligence training instability, financial market collapse, and engineered system overload. In each case, system evolution is expressed using PFL-X notation and compared to observed outcomes. Results indicate that high-density evaluation (>>O<<) consistently precedes collapse (X), supporting the claim that admissibility flow provides a transferable, pre-model structural diagnostic layer. The framework is domain-neutral and operates prior to domain-specific modelling, enabling cross-domain comparison and early identification of instability patterns.