Published March 31, 2026 | Version 0.9
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Fermion Mass Hierarchies from Prime Stability Conditions

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Pre-print presenting an empirical ansatz in which the adjacent-generation mass ratios of all twelve Standard Model fermions decompose into products of seven specific odd primes and powers of 2. Five physically motivated conditions select the prime set {3, 5, 7, 11, 17, 23, 29} uniquely by exhaustive enumeration, with no free parameters. The construction reproduces quark ratios within ~2σ, charged-lepton ratios within 0.1%, and predicts neutrino mass ratios of 7/3 and 21/4 consistent with oscillation data to 0.4%. The relationship to Kirchhoff elliptic vortex stability is noted as a structural parallel.

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Dates

Issued
2026-03-31
Pre-print presenting an empirical ansatz in which the adjacent-generation mass ratios of all twelve Standard Model fermions decompose into products of seven specific odd primes and powers of 2. Five physically motivated conditions select the prime set {3, 5, 7, 11, 17, 23, 29} uniquely by exhaustive enumeration, with no free parameters. The construction reproduces quark ratios within ~2σ, charged-lepton ratios within 0.1%, and predicts neutrino mass ratios of 7/3 and 21/4 consistent with oscillation data to 0.4%. The relationship to Kirchhoff elliptic vortex stability is noted as a structural parallel.

References

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  • [2] W. Altmannshofer and A. Greljo, "Recent Progress in Flavor Model Building," Annual Review of Nuclear and Particle Science 75 (2025), arXiv:2412.04549.
  • [3] G. Kirchhoff, Vorlesungen über mathematische Physik: Mechanik. Teubner, Leipzig, 1876.
  • [4] Y. Koide, "New view of quark and lepton mass hierarchy," Physical Review D 28 (1983) 252.
  • [5] C.D. Froggatt and H.B. Nielsen, "Hierarchy of quark masses, Cabibbo angles and CP violation," Nuclear Physics B 147 (1979) 277–298.
  • [6] A.E.H. Love, "On the stability of certain vortex motions," Proceedings of the London Mathematical Society 25 (1893) 18–43.