Obsessive Coherence — Volume I: Theoretical lineage, conditions of pertinence, structural axioms, and the Principle of Katashi

Obsessive Coherence — Volume I proposes and formally derives the Principle of Katashi: the set of mathematical conditions under which complex adaptive systems enter a state of structural crystallization — locked correlations, exhausted adaptive capacity, and active fragility modes — before any observable failure. The central thesis is that systemic instability originates from excess coherence, not from excess noise. When a system ceases to dissipate as fast as it accumulates structural pressure, it enters the regime named obsessive coherence. The question that motivates the framework is blunt: when an adaptive system has lost the capacity to adapt but has not yet failed, how can one recognize it?Volume I covers the theoretical and formal foundation of the Kappa program across four parts. Part I traces the scientific lineage from which the framework descends — Bénard, Prandtl, Lorenz, Mandelbrot, Schrödinger, Boltzmann, Shannon, Wheeler, Feynman, and Prigogine — establishing why dissipative structure theory, deterministic chaos, and variational principles form the necessary ancestors of a topological fragility diagnostic. Part II establishes the conditions of pertinence: the mesoscopic window and the mature phase that delimit when the framework applies. Part III derives the three structural axioms over which the Principle operates: the classical observable, adaptive capacity, and structural viscosity. Part IV states the Principle of Katashi proper through its three theorems — C1 (accumulation of structural pressure), C2 (structural arrow of time), and C3 (trigger-ready threshold) — and provides formal derivations, invariance proofs, and calibration methodology.The volume includes five technical appendices: formal derivations of C1, C2, and C3; proofs of invariance under component permutation, Lipschitz continuity, and IID noise cancellation; calibration and statistical significance protocols (KCPT, LOUO, bootstrap intervals); a methodological note on the Navier-Stokes analogy; and operational material including the complete empirical validation table, pseudocode for central metrics, and the obsessive attractor signature in LLMs.This book extends the paper Obsessive Coherence: A Domain-Agnostic Structural Signature of Fragility and a Layered Architecture for Predictive Monitoring (DOI: 10.5281/zenodo.19393239) by developing the theoretical structure and historical lineage that sustain the cross-domain empirical results reported there. It is Volume I of two; Volume II (in construction) will cover the layered diagnostic architecture and detailed domain-by-domain validation across financial markets, language models, educational systems, political networks, and atmospheric dynamics.Part of the Kappa Method ecosystem: Kappa-FIN (DOI: 10.5281/zenodo.19708131), Kappa-LLM (DOI: 10.5281/zenodo.18883790), Kappa-Radiante (DOI: 10.5281/zenodo.18940478), Kappa Method v2 (DOI: 10.5281/zenodo.19339548).David Ohio | Independent Researcher | odavidohio@gmail.com | CC BY 4.0