Structure-Sensitive Mathematics V: Physical, Quantum, and Artificial Intelligence Systems — Omega-Based Structural Monitoring and Pre-Failure Detection

Halil Özbil

Published Jun 14, 2026• 0 citations

Abstract

This work presents the fifth and final paper of the Structure-Sensitive Mathematics (SSM) research series, extending the Omega framework from mathematical foundations into physical modeling, quantum information, artificial intelligence systems, and reliability analysis. Building upon: Part I — Omega-Sensitive Function Spaces Part II — Omega-Banach and Omega-Hilbert Structures Part III — Omega-Operator Theory and Omega-Calculus Part IV — Omega-Topology and Omega-Geometry this study explores the application layer of Structure-Sensitive Mathematics. The central principle investigated is: Observable equivalence does not necessarily imply structural equivalence. The framework extends system representation from: x toward: (x, Ω(x)) where Ω represents a structure-sensitive functional combining geometric, informational, and complexity-related components. This paper introduces and discusses: • Omega-based physical field extensions • Structure-sensitive action principles • Omega-field equations • Quantum structural state discrimination • Connections with Quantum Structural Perturbation Framework (QSPF) • Structural decoherence indicators • AI model structural monitoring • Omega-based pre-failure detection • Structure-sensitive digital twin concepts Core formulations include: δ(S + λΩ) = 0 and: Ω = αG + βI + γC The proposed approach investigates whether systems that appear identical under classical measurements may contain hidden structural differences affecting future evolution, robustness, or reliability. Potential research connections include: • theoretical physics • quantum information science • artificial intelligence safety and reliability • complex adaptive systems • digital twins • predictive maintenance • structure-aware engineering systems This work does not replace existing physical, quantum, or computational theories. Instead, it proposes an additional structural analysis layer and defines open problems requiring experimental validation, domain-specific calibration, and empirical testing. Part V of V — Applications and Future Directions of Omega-Based Structural Analysis.

DOI: 10.5281/zenodo.20688962

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