Information-Theoretic Analysis of Metabolic Quench Events: A Case Study in State-Vector Transition

This technical memorandum examines the information-theoretic consequences of metabolic quench in biological neural networks. Part I presents a speculative mathematical framework for the unitary evolution of system correlation data following cessation of metabolic driving forces, employing concepts from Fisher information geometry, topological error correction, and modular theory of operator algebras. Part II provides a critical analysis of the physical plausibility of the framework, addressing thermal decoherence constraints, finite-system algebraic misapplications, and fast scrambling timescales. Part III concludes with a summary of mathematical consistency versus empirical feasibility. This work constitutes a theoretical exercise in applied quantum information theory and does not purport to establish empirical facts regarding subjective continuity.