A Structural Origin of the Charged-Lepton Hierarchy

This paper proposes that the charged-lepton mass hierarchy may originate from a dimensionless structural invariant of a neutral-parent carrier-defect architecture, prior to its effective Higgs–Yukawa read-out. The guiding principle is that indistinguishable admissible internal sectors carry equal primitive weight before physical carrier read-out. Applied to the charged-lepton root variables (me,mμ,mτ), this principle gives the Koide relation as an equal-power condition between a democratic parent component and a branch-splitting component. The Koide cone is therefore interpreted as a root-space representation of a discrete sector-power balance, not as a fundamental continuous mass geometry. The main quantitative result is an endpoint expansion for the small electron–muon mass ratio. In the proposed architecture, the electron is interpreted as a charged endpoint leakage of the lepton-facing branch, measured against the first exposed positive-closure environment. This leads to the charged endpoint towermemμch=132(4!−1)1+∑k=5∞∏n=5k2/n3(n!−1).