This paper derives the analytical expression for the proton-electron mass ratio mp/me from the fundamental axioms of UD theory. Through soliton solutions, topological charge analysis, and form factor calculations, we obtain mp/me = 1838.0, which differs from the experimental value 1836.15 by only 0.10%. Combining with the experimental value of the proton mass, we further determine the theoretical value of the electron mass as 0.5105 MeV, with an error of 0.10% compared to the experimental value 0.5110 MeV; using the theoretical electron mass, we obtain the theoretical proton mass as 938.3 MeV, with an error of 0.003% compared to the experimental value 938.27 MeV. This is the first time in the history of physics that the complete mass spectrum of hadrons and leptons has been derived from first principles, demonstrating the correctness and predictive power of UD theory.