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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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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1The Koide Formula as a Resolution Geometry Theorem: Deriving the Lepton Mass Relation from Dimensional Projection2026
  2. 2A Geometric Interpretation of the Koide Lepton Mass Relation Based on an Orientational Structure of Space2026
  3. 3A Unified Geometric, Variational, and Minkowski-Embedded Perspective on the Koide Leptonic Mass Relation2026
  4. 4A Geometric Origin of the Koide Relation: Lepton Generations and Mass Hierarchy from a Degree-Three Monopole Bundle2026
  5. 5Geometric Origin of the Lepton Mass Spectrum: The Koide Formula as a Null-Vector Condition in Split-Quaternionic Space (Part VII)2026