Triangle Based Geometric Semantic Modeling for Time Series Analysis

We formalize Triangle-based Geometric Semantic Modeling (TGSM), a novel approach to time-series analysis that encodes temporal transitions as geometric primitives. Consecutive observations are mapped to right-angled triangles, linking time span and change magnitude to a unified measure of movement strength. By organizing these primitives into directional classes and aggregating them across scales, TGSM provides a transparent bridge between raw signals and semantic structure. This framework offers a new lens for interpreting dynamic behavior and establishes an audit-ready foundation for semantic compression, model transparency, and robust feature design in explainable AI. The paper highlights the formulation, key derivations, and potential applications of this approach. Keywords: Time‑series geometry, Triangle primitives, Structural decomposition, Directional transitions, Semantic representation, Multiscale analysis