PRPFE: Operational Use and Interpretation

This paper presents the operational use of the Paton Recursive Pressure Field Equation (PRPFE) as a minimal method for evaluating system continuation under constraint. The PRPFE defines recursive structural progression, but does not operate independently. Its valid use requires integration with admissibility conditions and boundary constraints. The paper formalises how the equation is applied: defining system states, applying constraint coefficients, evaluating continuation, and identifying boundary conditions. It establishes a clear, domain-independent method for interpreting system behaviour, stability, and collapse. The PRPFE is positioned as a generator of candidate structural states, while admissibility determines whether those states can persist. Collapse is interpreted not as failure of the equation, but as constraint incompatibility, consistent with the Constraint-Incompatibility Collapse Law (CICL). This work functions as an operational clarification within the Paton System, bridging formal definition and practical application across physical, computational, biological, and cognitive domains.