Series Paper — SM-Line
Standard Model Series
SM-8: Quark Generation Structure from 600-Cell Distance Shells
All four quark masses to 2.1% RMS across four orders of magnitude from electron mass and 600-cell geometry
2.1% RMS across four orders of magnitude
Abstract: The 600-cell admits exactly four bonded distance shells — tetrahedron (V=4), icosahedron (V=12), dodecahedron (V=20), and icosidodecahedron (V=30) — separated by a structurally significant gap. These shells correspond one-to-one with CPP cage types for quark generations. A zero-free-parameter mass formula M_q = m_e (z/phi) V^(7/3) predicts the strange, charm, and bottom quark masses, and a post-gap z C_F = 16 multiplier predicts the top, reproducing all four quark masses to 2.1% RMS using only the electron mass, 600-cell geometry, and the SU(3) Casimir. The four-bonded-shells theorem and antipodal identification in the tessellated lattice constrain the Standard Model to exactly three generations.
- All four quark masses to RMS 2.1% from m_e alone
- Four bonded cage types theorem (exact)
- Three generations forced by 600-cell tessellation