On a Universal Truth Metric in Information-Theoretic Dynamical Systems

This paper presents a rigorous mathematical formalization of coherence as a universal truth metric within the framework of information-theoretic dynamical systems. We define coherence as normalized negentropy on finite probability spaces and prove it satisfies five axiomatic criteria for a truth metric: discriminability, objectivity, computability, universality, and self-consistency. We construct a six-variable cross-axis dynamical system governed by Filippov differential equations with discontinuous right-hand sides. Using Lyapunov stability analysis and LaSalle’s invariance principle, we demonstrate the existence of a unique globally asymptotically stable attractor corresponding to maximum coherence and zero impedance. The study also formalizes the thermodynamic cost of false models via Landauer’s principle and Kullback-Leibler divergence, providing a purely mathematical foundation for the structural identity of truth and low-entropy states.