A Geometric Interpretation of the Koide Lepton Mass Relation Based on an Orientational Structure of Space

This work presents a geometric interpretation of the Koide lepton mass relation based on a three‑degree‑of‑freedom orientational structure of space. In this framework, the charged leptons arise as three excitations of a single geometric object with two active and one stabilizing mode. The square roots of the lepton masses correspond to amplitudes of orientational twist, while the masses themselves correspond to frustration energy. The well‑known value Q=2/3 emerges naturally as a geometric ratio between active and total degrees of freedom. The approach offers an ontological explanation of the Koide relation and suggests that geometric orientation may form a deeper basis for lepton physics than currently assumed in the Standard Model. The text is intended as a concise standalone note and as part of a broader program exploring orientational dynamics of spatial structures.