A QDL Constraint on the Muon–Electron Mass Ratio from Koide Eigencone Closure and Relational Phase Quantization

This preprint develops a narrow Quantized Dimensional Ledger (QDL) constraint on the dimensionless charged-lepton mass ratio mₘu/mₑ. The construction begins with the Planck-normalized QDL mass-occupancy coordinate chiₘ = Gm²/ (hbar c) = (m/mP) ², so that square-root mass is proportional to the quarter-power occupancy amplitude chiₘ^ (1/4). The charged-lepton square-root mass vector is therefore interpreted as a QDL occupancy-amplitude vector. Balanced singlet/doublet flavor closure places this vector on the Koide eigencone, equivalent to Qₗ = 2/3. Koide closure alone fixes only the cone and leaves one angular degree of freedom, the phase theta. The paper introduces a minimal QDL relational phase constraint: the charged-lepton Yukawa map has a 3 x 3 relational generation ledger with nine entries, while the non-democratic hierarchy sector has rank two. The proposed phase residual Rₜheta (theta) = (9 theta - 2) ² therefore vanishes at thetaₗ = 2/9. Substitution of thetaₗ = 2/9 into the Koide-cone parametrization gives the radial-independent prediction (mₘu/mₑ) QDL = 206. 770315973. Using mₑ = 0. 51099895069 MeV and mₘu = 105. 6583755 MeV, the observed ratio is (mₘu/mₑ) ₒbs = 206. 768282708, giving a relative residual of 9. 83 x 10^-6. The paper does not claim to derive the full charged-lepton spectrum, the absolute mass scale, or a complete theory of flavor. Its claim is deliberately narrower: a minimal QDL phase constraint on the Koide eigencone fixes the radial-independent ratio mₘu/mₑ at the 10^-5 level. The manuscript includes explicit failure criteria, residual-status analysis, and a reproducible Python calculation.