Within the framework of a unified field theory based on a superdense (ρ_E ≈ 10^13 kg/m³), superfluid, and practically incompressible ether, we derive the proton-to-electron mass ratio m_p/m_e = 1836 as a consequence of the topology and mechanics of the ether. The electron is modeled as a single Hopf soliton, the proton as a three‑strand Borromean link. Pairwise (λ) and triple (μ) interactions, determined by Gauss integrals and the Milnor invariant, lead to a compression of the equilibrium proton radius to R_p ≈ 0.082 R_e. The cubic dependence of mass on radius (m ∝ R^3) gives (R_e/R_p)^3 ≈ 1814, while small spin and logarithmic corrections bring the ratio to 1836. The ether pressure P ∼ 10^25 Pa is derived from the Lagrangian of a superfluid condensate and is linked to the fine‑structure constant α. On cosmological scales, the effective pressure becomes negative, identifying it with dark energy. We predict that the proton radius measured in muonic hydrogen should be about 1.6% smaller than the value obtained from electron experiments, a prediction that can be tested in upcoming studies. Thus, the number 1836 ceases to be an empirical constant and becomes a consequence of the topological structure of the ether.