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.
James Reeves (Wed,) studied this question.