Obsessive Coherence

Obsessive Coherence v3 introduces the current mature formulation of the framework as a structural theory of fragility and a predictive architecture for finite-horizon hazard. The paper formalizes the characteristic relation F = 1 − κ(ψ) under a canonical spectral model, defines interpretable regime quantities such as the Kappa Number and Memory-Capacity Ratio, and validates the obsessive coherence signature across five domains. Its central new empirical result is a hazard model for EMERGENCY first-entry events: LSCC-augmented structural state reaches ROC-AUC 0.83 at 60 days in Leave-One-Universe-Out validation across 19 financial universes, versus 0.41 for state-only features. The paper also reports three negative results — noise-dominated daily erosion, uninformative trajectory entropy, and confounding by raw regime persistence — clarifying where the framework’s chronological power does and does not reside. Note: v2: Expanded reference version with full mathematical appendix, complete experimental tables, and improved documentation of the layered Kappa architecture, LSCC robustness, and cross-domain results. Core claims unchanged; presentation, reproducibility, and reference value substantially improved. This preprint presents Kappa as a new framework for understanding and monitoring structural fragility in complex systems. Its central thesis is deliberately counterintuitive: systems often do not become fragile through disorder, but through excessive coherence. When internal coupling becomes too concentrated, diversity collapses, and adaptive flexibility is depleted, the system enters a rigid and vulnerable regime that may persist long before visible damage appears. The article introduces this mechanism under the name obsessive coherence and develops it across the full Kappa research program — from structural theory to predictive instrumentation. It proposes a layered architecture for monitoring, separating three distinct but connected phenomena: geometric sensitivity, latent pre-damage organization, and realized structural damage. This distinction resolves a central ambiguity in early-warning research, where vulnerability and collapse are often treated as if they were the same thing. The manuscript also presents Kappa-SIG, the predictive extension of the framework, and its strongest latent result: the Latent Structural Crystallization Coordinate (LSCC), the dominant projection of a learned structural fingerprint. The LSCC provides robust complementary signal for pre-damage detection, especially in regimes where conventional baseline-dependent observability fails. Robustness analyses show strong cross-universe discrimination, temporal generalization, and clear separation from null baselines. To test the generality of the framework, the same mathematical pipeline is applied across five distinct domains: financial markets, large language models, educational engagement, political networks, and atmospheric dynamics. Across all five, stressed conditions consistently exhibit the same structural pattern: higher spectral concentration, greater rigidity, stronger leading-mode dominance, lower diversity, and stronger coupling. This cross-domain recurrence supports obsessive coherence as a general structural signature of fragility, rather than a domain-specific anomaly. Finally, the article describes Sentinel, the production-facing implementation of Kappa for prospective monitoring across 21 financial universes. Active cases illustrate the mature semantics of the framework: structural crystallization signals reduced adaptive margin, but realized damage still depends on sufficient triggering conditions. Taken together, this work positions Kappa not only as a theory of fragility, but as a practical architecture for layered predictive monitoring across complex systems.