What question did this study set out to answer?

This research aims to explore the connection between lepton mass ratios and geometric properties derived from the face Laplacian spectrum of the truncated octahedron.

March 25, 2026Open Access

Mass Ratios from the Face Laplacian Spectrum of the Truncated Octahedron

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Key Points

This research aims to explore the connection between lepton mass ratios and geometric properties derived from the face Laplacian spectrum of the truncated octahedron.
Derived the Koide identity and angle from the face Laplacian spectrum
Calculated lepton mass ratios m_μ/m_e and m_τ/m_μ with zero free parameters
Utilized geometric dimensions to inform predictions about mass ratios
Predicted lepton mass ratios to an accuracy of 10–70 ppm
Established a mathematical identity linking mass ratios to geometry of the truncated octahedron
Demonstrated that predictions can be made without any free parameters

Abstract

The Koide identity Q = 2/3 derived from ε = √ (dim T₂g − 1) = √2. The Koide angle θ = 2/9 derived from (λA₂u − λT₂g) /λA₂u = (9−7) /9. Lepton mass ratios m_μ/mₑ and m_τ/m_μ predicted to 10–70 ppm with zero free parameters. Both parameters derived from the face Laplacian spectrum of the truncated octahedron.

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Luke Martin

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Mass Ratios from the Face Laplacian Spectrum of the Truncated Octahedron

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Abstract

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