Charged-Lepton Mass Hierarchy from Neutral-Parent Koide Geometry in a Reconstruction Framework

The charged-lepton mass hierarchy remains unexplained in the Standard Model: the Higgs mechanism relates \(m_e\), \(m_\mu\), and \(m_\tau\) to three Yukawa couplings, but does not determine their ratios. This paper applies a minimal effective subset of a previously developed reconstruction framework, including carrier embedding, finite-action phase behavior, and codimension-two defect structure, to the charged-lepton mass problem. Charged leptons are modeled as carrier-embedded defect channels arising from a common neutral parent, and their masses are interpreted as quadratic residual responses. The natural variables are therefore root residuals rather than masses themselves. The main algebraic result is that Koide's relation is equivalent to equality between the democratic parent component and the orthogonal channel-splitting component of the charged-lepton root vector. This reduces the hierarchy to a one-angle problem on the Koide cone. The remaining angle is fixed by an effective weak-closure selector involving the neutron--proton mass difference, the democratic electron projection, the beta-continuum scale, the fine-structure constant as a \(U(1)\) carrier-dressing factor, and a finite positive-end recoil term. No continuous parameter is fitted. Using only \(m_e\), \(m_p\), \(m_n\), and \(\alpha\) as physical boundary inputs, the weak-closure selector gives \[m_\mu^{\rm pred}\simeq 105.6565~{\rm MeV}, \qquad m_\tau^{\rm pred}\simeq 1776.94~{\rm MeV}, \] with relative errors of approximately \(-0.0017\%\) and \(+0.0045\%\), respectively. The Koide-cone reduction is algebraic, while the weak-closure selector is presented as an effective boundary condition requiring future microscopic derivation. The result provides a falsifiable route by which the charged-lepton hierarchy may arise from neutral-parent root balance and weak closure rather than from three independent Yukawa parameters.