The Coherence Field: A Geometric Framework for Multi-Scale Physical Systems

The fragmentation of contemporary science—manifested in the incompatibilities between General Relativity, Quantum Mechanics, and complex non-equilibrium systems—suggests the absence of a unifying geometric description for coherence-driven phenomena across scales. In this programmatic working paper, we introduce Tonal Meta-Ontology (TMO) as a coherence-based geometric framework for organizing multi-scale physical systems. Central to this framework is the notion of a Coherence Field (Ψ), a complex order parameter whose evolution is constrained by a scale-invariant structural principle. We identify a representative variational formulation consistent with TMO axioms and demonstrate that it naturally induces a class of coherence-regulated dynamics. Within this framework, we show that a unified statistical evolution law emerges, classifying coherence behavior into three qualitative regimes—closure, criticality, and resonance. Across selected physical domains, existing empirical data appear consistent with the presence of a non-mean-field critical signature, suggesting a shared structural origin rather than domain-specific coincidence. The purpose of this paper is not to provide exhaustive proofs or domain-complete validations, but to establish a conceptual and geometric foundation upon which specialized theoretical, numerical, and experimental studies may be constructed. Detailed derivations, rigorous proofs, and domain-specific implementations are deferred to companion works. Aspects of this theoretical framework are subject to pending patent applications by Yunaverse, Inc. Keywords: Coherence Field Theory, Multi-Scale Dynamics, Critical Exponents, Navier-Stokes Regularity, Quantum Chemistry, Computational Framework, Geometric AI Alignment.