Cyclotomic-12 Structure in the Charged-Fermion Mass Spectrum

We present two structural mass relations that reduce the nine charged-fermion masses to two empirical scale inputs and identify their cyclotomic-12 and SU(5)/SO(10) origins. The TT relation (m_u_g/m__g) = (/6) 2^g + /8 holds against PDG masses at 0.37\% max-fractional-error across six -free inter-generational identities (null density 610^-6). The VV relation (m_d_g) = 139(m_u_g) - 76(m__g) - 514 holds at 0.17\% across all three generations (null density 10^-5). Combined with the Koide closed form Spivack2026_Koide, all nine charged-fermion masses are determined from two scalar inputs. The TT coefficient = /6 is the half-opening angle of the A_2 Weyl chamber (Lean-certified: angle\_alpha1\_omega1\_eq\_pi\_div\_six, zero sorry); the generation-doubling factor 2^g is proved via a binary cascade (Lean-certified). The VV coefficients (13/9, -7/6, -5/14) satisfy exact SU(5)/SO(10) group-theoretic identities (VV\_from\_GUT\_group\_theory, zero sorry) classified as structural facts [T]; the coefficient-value interpretation is classified [C] (see :vv_honest). A pre-registered three-null-test discipline accompanies each derivation. All Lean content is machine-checked at zero sorry in the ugp-lean library ugp-lean.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-16
DOI
https://doi.org/10.5281/zenodo.20711619
Primary Topic
Particle physics theoretical and experimental studies
Type
preprint
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preprint

Cyclotomic-12 Structure in the Charged-Fermion Mass Spectrum

Nova Spivack
Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
preprint

Cyclotomic-12 Structure in the Charged-Fermion Mass Spectrum

Nova Spivack
preprint en

Abstract

We present two structural mass relations that reduce the nine charged-fermion masses to two empirical scale inputs and identify their cyclotomic-12 and SU(5)/SO(10) origins. The TT relation (m_u_g/m__g) = (/6) 2^g + /8 holds against PDG masses at 0.37\% max-fractional-error across six -free inter-generational identities (null density 610^-6). The VV relation (m_d_g) = 139(m_u_g) - 76(m__g) - 514 holds at 0.17\% across all three generations (null density 10^-5). Combined with the Koide closed form Spivack2026_Koide, all nine charged-fermion masses are determined from two scalar inputs. The TT coefficient = /6 is the half-opening angle of the A_2 Weyl chamber (Lean-certified: angle\_alpha1\_omega1\_eq\_pi\_div\_six, zero sorry); the generation-doubling factor 2^g is proved via a binary cascade (Lean-certified). The VV coefficients (13/9, -7/6, -5/14) satisfy exact SU(5)/SO(10) group-theoretic identities (VV\_from\_GUT\_group\_theory, zero sorry) classified as structural facts [T]; the coefficient-value interpretation is classified [C] (see :vv_honest). A pre-registered three-null-test discipline accompanies each derivation. All Lean content is machine-checked at zero sorry in the ugp-lean library ugp-lean.

Zenodo (CERN European Organization for Nuclear Research)
Particle physics theoretical and experimental studies
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