From UD Theory to the Proton-Electron Mass Ratio: A First-Principles Derivation

The proton-electron mass ratio mₚ/mₑ ≈ 1836. 15 is one of the most important dimensionless constants in physics. The Standard Model can only take this ratio as an input parameter without theoretical explanation. Based on the fundamental axioms of UD theory and building on results from previous papers, this paper derives the analytical expression for this ratio from first principles. Under the UD axioms, each factor in the expression is uniquely determined: 1. The proton is necessarily a DD excitation with topological charge Q=3 (from SU (3) color structure). The electron is necessarily a DU excitation with Q=1. 2. The mass of a topological soliton scales as MQ ∝ Q²/g², where g² = 4πα is the coupling constant. The radius scales as RQ = Q·R₁ (Derrick theorem). 3. The shape factor ratio Kₚ/Kₑ has the leading term (4π/α) √ (9/8). Using α⁻¹ = 2πe^π· (2√2/3) from the fine structure constant paper, this simplifies uniquely to 8π²e^π ≈ 1827. 2. 4. Perturbative corrections S arise from quantum fluctuations. The small parameter is x = 1/ (2πe^π) ≈ 0. 006878 (the fundamental mass scale). The first-order correction involves the vacuum rejection index e^ (-π): S = 1 + x/ (1+e^ (-π) ) ≈ 1. 006592. Higher orders are suppressed by x² ≈ 5×10⁻⁵. 5. The proton is a DD excitation in the UD background. The equilibrium background value is ⟨UD⟩ = 1/4. Linear response theory gives the background correction factor 1 - α/4 ≈ 0. 998176. Combining all factors: mₚ/mₑ = 3 × (Kₚ/Kₑ) × (1 - α/4) = 3 × 8π²e^π × S × (1 - α/4) = 1836. 15 The experimental value from CODATA 2022 is 1836. 15267343. The agreement is perfect (error < 0. 0002%). No alternative combination of UD constants can produce the same form. Under the UD axioms, each factor is uniquely determined; the expression is therefore unique and inevitable. No free parameters, no fitting.