Φ₀: A Universal Initiation Threshold for Self-Sustaining Dynamics

This work introduces Φ₀ (phi-zero) as a universal initiation threshold through which complex systems transition from latent potential into self-sustaining dynamics. The paper formalizes a complete lifecycle of meaningful dynamics—latent state (Λ₀), initiation (Φ₀), sustained flow (Φ-flow), and de-coherence (Φ₋₁)-and presents the SEPH Kernel as a minimal, domain-agnostic execution layer capable of detecting and tracking this transition across physical, biological, cognitive, collective, and artificial systems. By explicitly defining the structural moment at which coherent dynamics begin, the framework addresses a foundational gap present across complexity science, artificial intelligence, and emergence theory. In the context of Artificial General Intelligence (AGI), Φ₀ provides a principled distinction between continuous processing and initiated, self-sustaining intelligence, reframing AGI as a transition in system dynamics rather than a product of scale alone. Beyond AI, the framework offers a shared structural language for understanding how complex systems—technological, social, institutional, and ecological—initiate, stabilize, and lose coherent direction. This work contributes a foundational initiation layer applicable across disciplines concerned with coherence, intelligence, and long-term system stability.