Mismatch Principle: A Geometric Diagnostic of Model Inconsistency in Complex Systems

This paper introduces the Mismatch Principle, a universal analytical frameworkfor detecting structural inconsistencies and anomalies in complex dynamical systems. Unlike traditional anomaly detection methods that focus on state-space outliers, theproposed framework evaluates the geometric alignment between two distinct descriptors of the same system: the physical realization (constrained flow) and the optimalmodel (theoretical geodesics). We define a divergence metric on a Riemannian manifoldthat quantifies systemic tension via angular misalignment. The principle is demonstrated across multiple domains, including medical hemodynamics (AAM-V11), robotics, and artificial intelligence, providing a domain-agnostic diagnostic signal derived frominternal model consistency. This paper introduces the Mismatch Principle, a universal analytical framework for detecting structural inconsistencies and anomalies in complex dynamical systems. Unlike traditional anomaly detection methods that focus on state-space outliers, the proposed framework evaluates the geometric alignment between two distinct descriptors of the same system: the physical realization (constrained flow) and the optimal model (theoretical geodesics). We define a divergence metric on a Riemannian manifold that quantifies systemic tension via angular misalignment. The principle is demonstrated across multiple domains, including medical hemodynamics (AAM-V11), robotics, and artificial intelligence, providing a domain-agnostic diagnostic signal derived from internal model consistency. Methodology ID: AAM-V1ARTSYBASHEVUAKHARKIVAIANALYSIS Methodology Name: Метод Арцыбашева (AAM-V1)