Integrated Structural Generation Theory (IGS): A Minimal Unified Framework for Emergence, Persistence, and Decay Across Scales

This work presents Integrated Structural Generation Theory (IGS), a minimal unified framework describing emergence, persistence, and decay across physical, biological, and artificial systems. Rather than modeling systems as collections of components, IGS interprets them as evolving structures governed by a generative chain: Difference → Fixation → Information → Meaning → Emergence → Persistence → Decay The framework is built on three core structural variables: - Structural persistence F(t)- Structural density C(x,t)- Connectivity Γ(t) A central concept is structural viability, defined as: R(E) = (C · Γ · dS_C/dt) / Θ(E) From this, structural lifespan is defined as: T_life = { t | R(E,t) > 1 } This provides a unified way to describe when systems emerge, remain stable, and decay. The framework is visualized through a complete set of figures (Fig1–Fig10), which cover: - Generative structure (Fig1)- Core variables (Fig2)- Structural dynamics (Fig3–Fig5)- Disease interpretations (Fig6–Fig8)- Structural phase space (Fig9)- Viability threshold crossing (Fig10) In particular, Fig9 introduces a structural phase space (F, C, Γ), where different systems and diseases are interpreted as trajectories, and Fig10 defines the boundary between persistence and decay through R(E,t)=1. All figures are fully reproducible using the provided Python script. This framework does not replace empirical data; it reorganizes its meaning, offering a unified structural interpretation of intelligence, biological organization, and disease.