Unified Wave Resonance Threshold Theory: From Microscopic Probabilistic Disorder to Macroscopic Deterministic Order

This preprint presents the initial version (v1.0) of the Unified Wave Resonance Threshold Theory, released primarily to establish a timestamped public record of the concept. The work addresses a central question in complex-systems science: how macroscopic deterministic order emerges from microscopic probabilistic disorder, and under what conditions. Its proposal is that, across physical, chemical, biological, astronomical and commercial domains, ordered structures arise when phase-coupled microscopic carriers — described here with the standard Kuramoto coupled-oscillator dynamics — cross a resonance threshold: a critical coupling strength combined with an energy-input threshold, beyond which microscopic disorder gives way to macroscopic deterministic order. The formulation seeks to accommodate both endogenous spontaneous order emergence and exogenous constraint-driven order evolution within a single set of dynamical equations. As a preliminary model, both the mathematical framework and the theoretical construct will undergo continuous refinement in subsequent versions. The theoretical background includes Haken's synergetics and Nicolis & Prigogine's self-organization theory; full citations are provided in the References section.