A First-Principles Derivation of the Three Lepton Masses from an Eleven-Dimensional Covariant Master Action

The Standard Model describes the electron, muon, and tau masses through the three positive singular values of its charged-lepton Yukawa matrix, but does not determine their common scale and hierarchy from gauge symmetry alone. This work derives them within the charged-lepton branch of an eleven-dimensional information-projection theory represented by a seven-term covariant master action. The electron is identified by its representation and geometric support before its mass is evaluated. A common constrained stationary reduction then generates one positive operator on the three-dimensional family space, \[K_{}ʳᵉˢᵗ=κ_e(P_e+eg_μP_μ+eg_τP_τ).\] Here the mutually orthogonal projectors select the three family lines, \(κ_e>0\) determines their common scale in the reference-frequency convention, and \(g_μ,g_τ\) determine their logarithmic separations. The operator is dimensionless; its physical static mass operator is \[{hνCs}{c^2}K_{}ʳᵉˢᵗ.\] Both the scale and the gaps are generated by the reduced action, rather than assigned to reproduce the measured masses. A matched sector containing no charged lepton fixes the relative rest-energy origin. The same temporal generator and approximation connect this energy with its Noether, inertial, and spectral representations on the domains established in the paper. Coupling the retained states to the full complementary spectrum produces the causal/open result. A separate four-dimensional local effective action, with explicitly matched finite inputs, gives the complete charged-lepton two-point calculation within the declared action and one-loop order. Its strict first-insertion one-loop masses are approximately \[9.13873×10⁻³¹\,kg,1.88734×10⁻²⁸\,kg,3.17833×10⁻²⁷\,kg,\] respectively. Their root-mean-square relative residual against the fixed comparison masses is \(0.29326%\), a comparison statistic rather than a theoretical uncertainty. The conditional additive hybrid is reported separately and does not replace this local result. The measured lepton masses are not calibration inputs, and the branch, coefficients, signs, interactions, and subtraction conventions are not retuned after comparison. Because those masses were historically known, the result is a first-principles postdiction within the specified parent theory. Its physical content is a common spectral geometry: distinguishable family directions acquire their scale and separation within one reduced operator, whose relative energy and specified dynamical completions are read as charged-lepton mass.