The Universal Adaptive Equilibrium Principle (ULAE): A Recurrent Attraction to the Stability Boundary in Driven–Dissipative Systems

Abstract This work presents the Universal Adaptive Equilibrium Principle (ULAE), a theoretical framework proposing that driven-dissipative systems with local negative feedback and limited propagation tend to self-organize near their stability boundary ($\rho \approx 1$). Unlike other "knife-edge" models, the ULAE mathematically demonstrates that the stability boundary identified by the Universal Stability Principle (USL) acts as a recurrent attractor. This study unifies key concepts such as self-organized criticality (SOC), dissipative adaptation, and "edge-of-chaos" dynamics. Research Highlights: Multidisciplinary Validation: The principle has been tested across seven distinct regimes, including Gray-Scott reactions, 3-SAT optimization, neural network learning, Conway's Game of Life, and the Ising model. Quantitative Results: A strong alignment is observed in continuous and algorithmic domains, while discrete and stochastic systems show consistent qualitative trends following the application of metric refinements. Falsifiable Predictions: The document offers verifiable predictions regarding return times after perturbations, hysteresis areas, and finite correlation lengths. This principle provides a physical basis for understanding why biological, computational, and engineered systems maintain robustness and functionality by operating near critical phase transitions. Keywords: Self-organization, Homeostasis, Stability transitions, Limited propagation, Driven-dissipative systems, Recurrent attractors.