The Genesis-Integration Principle (GIP): A Universal Mathematical Framework for Evolution Across Biological, Technological, Social, and Cosmic Systems

The Genesis-Integration Principle (GIP) is a universal mathematical framework that describes evolutionary dynamics across biological, technological, social, and cosmic systems. GIP defines evolution as the dynamic interplay between genesis (G) and integration (I), capturing the essential forces driving systemic transformations. The model comprises three distinct evolutionary phases: short-term exponential growth, mid-term sigmoidal transitions, and long-term power-law stabilization, providing a systematic framework applicable across diverse domains.Unlike domain-specific models, GIP provides a unified approach to understanding system evolution, growth-state transitions, and stabilization. Its dynamical equations effectively describe various evolutionary trajectories, validated empirically in biological speciation, technological innovations, economic cycles, and cosmic phenomena. Future research should explore interdisciplinary applications, refine parameter estimation, and extend empirical validations. Integrating GIP into complexity science can enhance the comprehensive understanding of long-term systemic evolution, facilitating interdisciplinary collaboration.