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May 16, 20260 citationsOpen Access

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

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NKNicholas Kellogg

Key Points

  • To explore the geometric interpretation of the Koide formula in frequency space and its implications for lepton mass ratios.
  • Introduced a new interpretation using geometric principles related to the Koide formula.
  • Analyzed the relationship between mass square roots and field amplitudes.
  • Investigated the constraints imposed by the formula in frequency space.
  • Validated the Koide formula's relation at 0.000923% precision.
  • Demonstrated that mass square roots correspond to field amplitudes in quantum field theory.
  • Provided insights that reshape the understanding of mass ratios in the context of harmonic geometry.

Abstract

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...

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Cite This Study

Nicholas Kellogg (2026) studied this question.

synapsesocial.com/papers/6a0809f1a487c87a6a40bd72https://doi.org/10.5281/zenodo.20173367
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