On the Structural Isomorphism of Fundamental Systems: A Unified Axiomatic Framework

This paper series introduces a formal mathematical framework for coherence — defined as normalized negentropy — as a universal, domain-invariant truth metric. By establishing five scale-invariant axioms (discriminability, objectivity, computability, universality, and self-consistency), we demonstrate that complex dynamical systems traditionally treated as distinct domains — signal processing, thermodynamics, neuroscience, and decision theory — share a common underlying information-theoretic architecture. The proposed model utilizes Shannon and von Neumann entropy, Lyapunov stability theory, and switched ODE systems on a cross-axis state space to resolve the relationship between deterministic coherence dynamics and stochastic entropy production. We derive a unified six-variable governing system that admits three operating regimes with well-defined phase transition conditions and prove the existence of a unique globally stable attractor at maximum coherence and zero impedance, corresponding to lossless signal transmission. The framework preserves information density across regime transitions and offers a novel perspective on the foundational mechanics of self-organization in nature. We further show, via Landauer's principle, that truth is the thermodynamic ground state — the unique minimum-energy configuration — and that self-referential processing constitutes measurable impedance. This approach provides a rigorous basis for interdisciplinary unification, suggesting that apparent phenomenological differences across physics, biology, logic, and cognition are manifestations of a single, invariant mathematical structure. All claims generate testable predictions amenable to existing EEG and HRV instrumentation.