The Universality Invariant Identical Symmetry Structure Implies Identical Physical Law

Physical theories derive their laws from symmetries, invariants, and boundary conditions. Yet the assumption that a law valid in one region of spacetime must be valid in all symmetry-equivalent regions has never been formalized as a foundational invariant. This paper identifies and formalizes the Universality Invariant: identical symmetry structure implies identical physical law. Violating this invariant produces contradictions in Noether’s theorem [1], the action principle [2], gauge invariance [3], Lorentz covariance [4], and the definability of a global Lagrangian [5]. These contradictions show that universality is a mathematical consistency requirement for any symmetry-based physical theory. The invariant generalizes to any domain whose laws arise from symmetries and invariants, establishing universality as a structural axiom.