QDL Charged-Lepton Mass Spectrum: A Synthesis of Derived Structure and Phenomenological Radial Closure

This paper presents a consolidated Quantized Dimensional Ledger (QDL) synthesis of the charged-lepton mass-spectrum program. The central aim is to distinguish the structural layers derived within QDL from the radial layers that remain phenomenological diagnostics. The paper begins from the QDL mass-occupancy coordinate chi_m = Gm^2/(hbar c) = (m/m_P)^2, showing that square-root mass is proportional to the quarter-power occupancy amplitude chi_m^(1/4). In this representation, the charged-lepton square-root mass vector becomes a QDL occupancy-amplitude vector. The charged-lepton generation space is decomposed into a democratic singlet and hierarchy doublet, R^3 = 1 + 2. Balanced irreducible-channel closure is shown to be equivalent to the Koide relation, and this balance is derived from maximum irreducible-channel entropy. The resulting Koide eigencone is then supplemented by a QDL relational phase-closure rule. Using the charged-lepton 3 x 3 Yukawa relational ledger and hierarchy transport count, the phase residual C_theta(theta) = (9 theta - 2)^2 selects theta_l = 2/9. This gives a radial-independent prediction for the muon/electron mass ratio at the 10^-5 level. The radial layer is treated more cautiously. The Koide-cone trace identity gives M_l = (m_e + m_mu + m_tau)/6, but this uses the observed charged-lepton trace. A leading electroweak-electromagnetic radial ansatz M_l^(0) = alpha v/(4 sqrt(2)) is accurate at the percent level. A phenomenological phase-leakage diagnostic reduces the radial residual to approximately 2.10 x 10^-5, and the remaining residual is expressed as an effective charged-lepton closure coupling. These radial steps are explicitly identified as diagnostic and interpretive rather than independently derived first-principles results. The paper also states sector-admissibility boundaries preventing naive transfer of the charged-lepton formula to quarks or neutrinos, where confinement, renormalization scheme, mixing, neutral-sector structure, and threshold ledgers must be specified. The bounded conclusion is that QDL derives the charged-lepton occupancy-amplitude Koide eigencone and relational phase rule, while the absolute radial scale remains an open electroweak-electromagnetic closure problem.