Semantic Phasor Theory: A Unified Spectral Model of Meaning and Cognitive Structure

This work introduces semantic phasor theory, a mathematical framework that represents meaning as spectral structure. The theory extends spectral semantics by unifying concepts from AI, cognitive science, and signal processing into a single operator‑theoretic model. Within this framework, any semantic domain can be expanded in a spectral basis, with complex coefficients interpreted as semantic phasors whose magnitudes and phases encode the contribution and alignment of each semantic mode. This generalizes classical phasor analysis to abstract meaning spaces and provides a coordinate‑free alternative to high‑dimensional embedding methods. Semantic similarity, interference, and compositionality emerge naturally from the spectral decomposition. A worked example on a finite semantic subdomain demonstrates the full semantic‑phasor pipeline. The result is a rigorous and unified foundation for modeling meaning through spectral operators.