Mass Ratios from the Face Laplacian Spectrum of the Truncated Octahedron

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