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) = (π/6)· 2^g + π/8 holds against PDG masses at ≤ 0.37\% max-fractional-error across six β-free inter-generational identities (null density 6×10^-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~, all nine charged-fermion masses are determined from two scalar inputs. The TT coefficient α = π/6 is the half-opening angle of the A_2 Weyl chamber (Lean-certified: \_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 ( \_from\_GUT\_group\_theory, zero sorry) classified as structural facts [T]; the coefficient-value interpretation is classified [C] (see ). A pre-registered three-null-test discipline accompanies each derivation. All Lean content is machine-checked at zero sorry in the -lean library~.