Charge-Assigned Exponents in Koide-Type Mass Relations for Neutrinos, Charged Leptons, and Quarks

This work presents a phenomenological framework for four three-family fermion spectra: light neutrinos, charged leptons, down-type quarks, and up-type quarks. For a positive triplet m and a real exponent q, it defines p_i(q) = m_i^q / Σ_j m_j^q and R_q = Σ_i p_i(q)^2. The framework contains two empirical postulates. The first assigns, through the charges of explicitly specified carrier fields, q_ν = 1, q_e = 1/2, q_d = −1/2, and q_u = −1/4. The second imposes Rq_f = 2/3. Four homogeneous relations of degree zero follow, one of which is the Koide relation. Monotonicity and uniqueness, the geometry and complete parametrization of the balance cone, the cubic invariant, the third-mass formula, and the lower bound on the spectral span are established. Anomaly cancellation for N_c colors produces the ratios 1, 2, N_c − 1, and N_c + 1; the additional requirement that they belong to a single dyadic scale selects N_c = 3. Base two is not attributed to anomaly cancellation alone. The three charged sectors are tested within a stated mass prescription. The quark agreement is scheme sensitive and is not presented as a renormalized identity. For neutrinos, the oscillation splittings turn the q = 1 balance condition into an equation with one unknown: it has a unique solution for normal ordering and none for inverted ordering. With the updated inputs, the result is Σ_i m_i = 62.65 meV.