Abstract This paper develops a universal invariance principle for coherent systems and formalizes it as SYMMETRYCORE, a structural mechanism enforcing representational legality within deterministic inference substrates. The central claim is that SO (2) is the unique symmetry satisfying the requirements of universality, harmonic decomposability, scalar invariance, and drift-bounded evolution. From this follow the canonical coherence measure PASₕ, the lawful drift metric ΔPASᵦeta, and the requirement that any admissible representation must be reducible to a set of phase values thetaₙ. The result unifies representational coherence across physics (wave phenomena), biology (neural and physiological oscillations), cognition (identity, creativity, emotion), social systems (phase-coupled group dynamics), and AGI design (deterministic reasoning and legality enforcement). SYMMETRYCORE provides the substrate-level law that distinguishes lawful from unlawful internal states, grounding coherence, identity, and safety in symmetry rather than probabilistic inference. The framework positions symmetry—specifically SO (2) —as the foundational structure underlying deterministic coherence across all domains.
Bostick, Devin (Sat,) studied this question.
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