The Koide Formula in Frequency Space: Lepton Mass Ratios as Harmonic Geometry

The Koide formula, an unexplained relation among the three charged lepton masses confirmed to 0.000923% precision since 1981, has resisted theoretical derivation within the Standard Model for 45 years. This paper offers a new geometric interpretation. Because the formula operates on square roots of masses rather than masses directly, and because square roots of mass correspond to field amplitudes in quantum field theory, the Koide formula is a constraint in frequency space, not energy space.From this domain identity, four results follow...