
The note presents a compact geometric mass formula for the charged fermions based on regular-heptagon spectral data and a fixed cubic three-root spectrum. The three generations are identified with the roots of the polynomial alpha^3 + alpha^2 - 2 alpha - 1 = 0. Sector-dependent coefficients are generated from a common discrete label assignment for the fermion sectors. The charged-sector reference masses are not fitted independently, but are obtained from the Higgs vacuum expectation value v = 246.22 GeV through an exponential damping law M_ref^(f) = (v/sqrt(2)) exp(-Delta^(f)), with Delta^(f) = k0 - phi r_f - Q_f^2/sqrt(2) and k0 = 6 + 7u - 2u^2, where u = 2 sin(pi/7). For the nine charged fermions, the resulting predictions reproduce the observed hierarchy with a global root-mean-square deviation of 5.7%. This deposition contains the manuscript and a reference implementation used to generate the reported numerical results.
charged fermion masses, flavour hierarchy, Higgs vacuum expectation value, heptagon geometry
charged fermion masses, flavour hierarchy, Higgs vacuum expectation value, heptagon geometry
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