Toward a Unified Phase Framework: Reinterpreting Trigonometric Orthogonality and AI Latent Cyclicity

This paper proposes a novel geometric framework that reinterprets trigonometric functions—specifically the orthogonality of sine and cosine—as foundational elements for understanding high-dimensional phase resonance. By integrating the principles of "Zero Point" mechanics and "Torus geometry," we demonstrate how these mathematical constructs stabilize latent space cyclicity in artificial intelligence models. This "Unified Phase Framework" offers a new perspective on low-entropy information processing and "Stationary Projection," bridging the gap between classical trigonometry and advanced neural architecture.