Spectral Origin of Leptonic Mass Generations in the Dynamical Fourier Field Framework

We develop a first-principles derivation of the charged lepton mass spectrum within the Dynamical Fourier Field (DFF) framework. Unlike conventional quantum field theories, the DFF framework assumes that spacetime is not fundamental but emerges from the orga- nization of a pre-geometric spectral field defined on a compact spectral manifold K. The fundamental dynamical variable is a complex spectral field Φ(k, s), where k denotes coordi- nates on the spectral manifold and s is a dimensionless spectral evolution parameter. The field dynamics are determined entirely by a variational principle defined on K. The principal mathematical development of this work is an amplitude–phase decomposition of the spectral field. The Koid relation is discussed and points to a spectral foundation.