Information-Geometric Context Window Governance for Large Language Models via Observer Entropy and the Cognitive Phase Law (CPL 4.0)

This document introduces a phase-aware control framework for managing context windows in Large Language Models (LLMs). The method is based on the Law of Cognitive Phases (CPL 4.0) and models an LLM as a discrete-time dynamical system governed by entropy and stability metrics. A threshold policy regulates context growth, memory compression (summarize / chunk), and decoding parameters. The framework provides: * a hard invariant upper bound on context length, preventing entry into latency-throttled regimes,* a high-probability bound on time spent in degraded (Fragmentation) states,* explicit, calibrable constants derived from operational logs. The results are formal and constructive. The framework is intended for deployment in production LLM systems where context scaling, latency spikes, and stability degradation are critical constraints. Implementation and integration guidelines are available at:https://github.com/Khomyakov-Vladimir/llm-context-window-governance Version 2.0. Resolved structural defects P1–P5: replaced axiomatic surrogate entropy with KL-geometric observer entropy grounded in the Bridge Theorem (doi:10.5281/zenodo.19080663); proved sub-Gaussianity of composite Lyapunov noise; corrected proof gaps in induction and martingale arguments. Removed non-academic content.