The Koide Relation and Lepton Mass Hierarchy from Phase Coherence

The remarkable precision of the Koide relation among the charged lepton masses has long hinted at a deeper organizing principle underlying the mass spectrum of elementary particles. In this work, we show that the Koide formula emerges as a special case of a universal phase coherence law governing free, massive particle states, each modeled as a topological soliton of a temporal flow field. Each such particle contributes a complex phase vector with amplitude proportional to the square root of its mass and orientation set by an internal angle. The total interference amplitude defines a coherence quantity that partitions the spectrum into orthogonal leptonic and bosonic sectors. Crucially, we show that leptons must be assigned a topological weight of 2 due to their spinorial soliton structure: their moduli space admits a nontrivial double cover (π_1(M_1) ∼= Z_2), leading to fermionic statistics and wavefunction antisymmetry under exchange. Bosons, by contrast, carry topological weight 1, as their configuration spaces are singly connected. This two-weight structure yields an exact coherence partition: Q_ℓ = 2/3, Q_B = 1/3, and Q_total = 1, reproducing the Koide formula as a topological identity rather than an empirical coincidence. A small residual deviation from exact balance is observed, which may reflect higher-order corrections or spectrum incompleteness. This solitonic coherence framework provides a novel, topologically grounded lens on mass generation, with implications for both theory and experiment.