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.
Andrew John Paton (Mon,) studied this question.
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