Charged-Lepton Mass Hierarchy Law

We derive a closed no-target mass-ladder law for the charged leptons within an admitted three-shell Relator/Alpha source ledger and a scalar determinant-normalized Schur/Feshbach sector. In this framework, the electron, muon, and tau are not assigned different charged-current cores. They are the shell \ (n=1, 2, 3\) realizations of the same Gaussian electron Relator core. The charged-current core and the path-dependent finite prefactors remain at the electron anchor. Changing the admitted shell changes only an internal Relator exponent-slot Alpha coordinate. It does not define a new QED running coupling and it is not inserted as an additive correction to a mass logarithm. The common electron readout has the form \ (mₑ=Mₚ\, Cₚ () \!-R, R=8. \) For an admitted charged shell \ (n=2, 3\), the same prefactor is kept at the electron anchor and only the exponent-slot coordinate changes, \ (mₙ=Mₚ\, Cₚ () \!-R ₑ, ₍. \) Thus the physical mass logarithm is read only after the shell source has been converted into a bare affine source load, Schur/Feshbach dressed, and mapped back to the Relator exponent slot. The shell ledger supplies a positive shell-admission ratio \ (ₙ\) and its bare readout \ (Tₙ=ₙ, \) where \ (Tₙ\) is not a physical mass logarithm. It is converted into the bare affine load \ (₂, ₍\), dressed into \ (ₙ\), and only then read as \ (L₌, ₍= A ₑ^aff\! (ₙ). \) The determinant sector is written uniformly for both branches as \ (Dₙ=2+ L^lightₙ-34\, H^heavyₙ+^dynₙ. \) Here \ (L^lightₙ\) is the retained lower-sector determinant response, \ (H^heavyₙ\) is the upper-heavy Schur/Stieltjes response, and \ (^dynₙ\) is the normal-collar determinant tail. In the admitted three-shell closure, the tau branch is terminal, while the muon upper response is the normalized rank-one terminal heavy return evaluated self-consistently at the solved output logarithms. With \ (A=R=8, ₙ=Cₔₕ^ (₆₀ₔₒₒ) n+1 Dₙ, Cₔₕ^ (Gauss) =12 (2+ ₄), \) the resulting compact mass-log law is \ (L₌, ₍ₙmₑ= A\, Tₙ A (1-ₙ) +ₙ Tₙ, n=2, 3. \) The only supplied dimensionless theory input in the numerical audit is \ (^-1\). Measured \ (m_\) and \ (m_\) enter only as external comparison values after the dimensionless ratios have been computed, and \ (mₑ\) is used only as the final MeV conversion scale. The no-target evaluation gives \ (L₌, =5. 33159877458397, L₌, =8. 15399066072771, \) or \ (m₌䂰=206. 768285919222, m₌䂰=3477. 22785082421. \) With \ (mₑ=0. 51099895069\, MeV\), these become \ (m_=105. 658377140693\, MeV, m_=1776. 85978308121\, MeV, \) corresponding to \ (+0. 713\) and \ (-0. 780\) relative to the stated comparison values. No \ (Tₙ\), \ (₂, ₍\), \ (ₙ\), \ (Dₙ\), \ (ₙ\), \ (L₌, ₍\), or charged-lepton mass is fitted or supplied as an input.