The Universal Resonance Model (URM): A Mathematical Kernel for Dynamic Disease Systems

This paper defines the mathematical kernel of the Universal Resonance Model (URM), a dynamical systems framework that conceptualizes disease as instability, coupling, and transition across interacting physiological subsystems. The kernel provides a renderer-independent, text-first specification of core state variables, operators, and stability conditions, enabling reproducible implementation across clinical research, computational modelling, and AI-based decision support. This document serves as the formal reference layer for applied URM work, including clinical metrics, geometric templates, and AI integration frameworks, while intentionally separating theory from implementation.