A Three-Phase Generative Structure Model: Formalization of Dynamic Static Breathing Cycles

We introduce a three-phase generative structure model consisting of Dynamic, Static, and Breathing phases. This model captures a scale-invariant rhythm observed across historical, social, ritual, and physical systems. We formalize the model as a recursive operator acting on structured states, and show that the resulting dynamics exhibit fractal self-similarity. The framework provides a minimal mathematical foundation for describing generative cycles that alternate between differentiation, stabilization, and reintegration.