The Universal Stability Law by Limited Propagation — Version 3 (with Computational Validation)

🇬🇧 English AbstractThis work proposes a Universal Stability Law by Limited Propagation, unifying stability criteria across complex systems.The principle states that a system remains stable when local propagation F is slower than local containment or damping C: F < C → stableF = C → criticalF > C → unstable This rule has been qualitatively validated in diverse domains — coupled oscillators, neural networks, ecosystems, traffic models, and electrical grids — showing how local propagation limits predict global stability.The model extends the previous works Principle of Limited Propagation by Muñoz and Triangular Adaptive Coloring, providing a unifying mathematical framework for predictability and complexity. 🇪🇸 Español ResumenEste trabajo propone una Ley Universal de Estabilidad por Propagación Limitada, que unifica los criterios de estabilidad en sistemas complejos.El principio establece que un sistema se mantiene estable cuando la propagación local F es más lenta que la contención o amortiguación local C: F < C → estableF = C → críticoF > C → inestable Esta regla se ha validado cualitativamente en distintos dominios — osciladores acoplados, redes neuronales, ecosistemas, tráfico y redes eléctricas — mostrando cómo los límites locales de propagación predicen la estabilidad global.El modelo amplía los trabajos anteriores Principio de Propagación Limitada de Muñoz y Coloración Adaptativa Triangular, ofreciendo un marco matemático unificador para la predictibilidad y la complejidad. Version note / Nota sobre la versión This record corresponds to Version 2 (October 2025), fully revised and expanded in English. It includes analytical formulation, corrected figures, and a unified mathematical framework for the principle $F/C < 1$.Este registro corresponde a la Versión 2 (Octubre 2025), revisada y ampliada, con formulación analítica, figuras corregidas y un marco matemático unificado para el principio $F/C < 1$. Version 3 (October 2025):This version introduces a computational validation of the Universal Stability Law by Limited Propagation, confirming numerically that the stability frontier occurs at F/C = 1.A discrete dynamical network was simulated and analyzed, demonstrating exponential decay for F/C < 1, marginal equilibrium for F/C ≈ 1, and exponential growth for F/C > 1.A conceptual figure has been added to illustrate these regimes on a log-scale evolution plot. The Universal Stability Law proposes that stability in any complex system is maintained when the effective propagation F remains below the intrinsic damping C: F < C → stableF = C → criticalF > C → unstable This version unifies analytical formulation, computational verification, and graphical representation under one document.