The Coupling Factor F. A Comprehensive, Operational Framework for Collective Systems

This document presents a comprehensive, operational framework for the coupling factor F, a topological property that modulates the strength of quantization constraints in complex collective systems. It integrates empirical observations, theoretical derivations, and practical protocols for calculating F across domains such as neurobiology, thermodynamics, astrophysics, psychology, and sociology. {} Preliminary applications suggest that systems with F in the approximate range $[0.05, 0.15]$ tend to exhibit stable, coherent dynamics; values outside this range correlate with pathological or unstable states. The framework is designed to be immediately usable by researchers with standard computational tools, while providing a clear path for deeper theoretical exploration and experimental validation.