Semantic Phase Theory: An Information-Theoretic Framework for Meaning and Context

This paper introduces Noetica Theory, a meaning-phase model in which semantic entities are represented as wave functions defined over context-dependent phase spaces. We define raw and normalized meaning wave functions, noetica energy, semantic entropy, semantic free energy, and semantic interference, and we formulate a self-referential context update mechanism together with an energy conservation principle. We then connect this mathematical framework to large language models (LLMs), providing an interference-based interpretation of embeddings, Attention, prompt-induced contextual modulation, and hidden-state trajectories. The proposed framework offers a unified perspective on meaning, context, and the behavior of generative models. Code and experimental implementations related to this work are available at: https://github.com/noeticaresearch-del/noetica-research