PRPFE — Complete Structural Unification Framework (v1.1 Formal Edition)

This work formalises the Paton Recursive Pressure Field Equation (PRPFE) as a constraint-modulated second-order recurrence whose eigenvalue structure defines regime classes corresponding to classical stability (GR-like behaviour), marginal oscillatory persistence (QM-like behaviour), and divergence (instability/chaos). The framework provides a structural unification of classical, quantum, and scale-transition behaviour via stability classification rather than direct equation derivation. PRPFE is positioned as the Tier-5 generative machinery expression within the Paton System and operates under admissibility constraints. This version strengthens mathematical formalism and clarifies scope boundaries without claiming UV completeness, renormalisability proof, or experimental confirmation.