Structural Admissibility and Regime Stability: Invariant Preservation, Threshold Logic, and Cross-Domain Integration

This paper formalises regime stability across physics, engineering, and complex systems as a function of invariant-preserving admissibility thresholds. Rather than proposing new physical laws, the Paton System is articulated as a structural integration framework clarifying how dimensionless invariants, conserved quantities, and load-distribution constraints govern lawful continuation. Regime continuity is expressed through bounded inequality conditions on scale-bridge invariant functionals κ. The distinction between invariant preservation and analytic compressibility is clarified using the classical three-body problem. Stability, chaos, and collapse are shown to be governed by invariant-bounded continuation rather than degradation of law. The contribution is structural integration rather than empirical novelty.