The Koide Relation as a Geometric Property of Layer 19 in TMD

This paper presents a geometric interpretation of the Koide relation within the framework of Triadic Model Dynamics (TMD). Layer 19, the first fully stable triadic configuration, naturally supports three structurally equivalent orientational states. These states correspond to the electron, muon, and tau. The masses of the leptons arise as monotonic functions of the compression of their orientational vectors. The Koide relation is shown to be equivalent to the statement that the compression vector of the three leptons forms a 45° angle with the uniform reference state of layer 19. This interpretation does not rely on dynamical transitions between leptons but instead reveals the geometric structure underlying their mass pattern. The result provides the first ontological explanation of the Koide relation, historically regarded as an unexplained empirical coincidence.