Within the framework of a unified field theory based on a super- dense (ρE ≈ 1013 kg/m³), superfluid, and practically incompressible ether, we derive the proton-to-electron mass ratio mp/me = 1836 as a consequence of the topology and mechanics of the ether. The elec- tron 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 Rp ≈ 0.082Re. The cubic depen- dence of mass on radius (m ∝ R3) gives (Re/Rp)3 ≈ 1814, while small spin and logarithmic corrections bring the ratio to 1836. The ether pressure P ∼ 1025 Pa is derived from the Lagrangian of a superfluid condensate and is linked to the fine-structure constant α. On cos- mological 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 ob- tained 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.