Balanced Flavor Closure and the Koide Charged-Lepton Relation in QDL Occupancy-Amplitude Space

This paper gives a self-contained Quantized Dimensional Ledger interpretation of the empirical Koide charged-lepton mass relation. In QDL, mass is represented by a Planck-normalized occupancy coordinate, so the square-root mass vector appearing in the Koide relation becomes a quarter-power occupancy-amplitude vector. The three charged-lepton generations are decomposed into a democratic singlet channel and a hierarchy doublet channel. The paper introduces balanced irreducible flavor closure as a QDL admissibility axiom: the singlet and doublet components of the charged-lepton occupancy-amplitude vector carry equal squared norm. This condition is shown to be exactly equivalent to a 45-degree angle between the occupancy-amplitude vector and the democratic flavor axis, and therefore exactly equivalent to the Koide relation. Taking the electron and muon masses as inputs, the positive charged-lepton branch gives a tau-mass completion of 1776.969 MeV, within roughly one quoted uncertainty of the Particle Data Group value. The manuscript does not claim to discover Koide or to derive all charged-lepton masses from first principles. Its contribution is to formulate Koide as a QDL occupancy-amplitude closure condition, define the corresponding admissibility functional, justify charged leptons as the proper first test sector, and explain why quarks and neutrinos require additional scheme, mixing, and neutral-sector closure rules.