Emergence of Spacetime and the Mass Hierarchy via 3D Topological Soliton Solutions

We present a deterministic, bottom-up topological field framework in which spacetime metric, gauge charge and invariant rest mass emerge from a single elastic vacuum continuum. Cosmic evolution is modeled as a sequence of recursive scale transitions (G0.n), from a primordial low-frequency state to the subnucleonic regime of the present epoch (G0.8), driven by exponential topological bifurcation and strict global charge neutrality (ΣQ ≡ 0). Fundamental fermions are modeled as quantized 3D topological solitons (Hopfions, T2,3 torus knots) of the Faddeev-Skyrme Lagrangian. We propose a geometric interpretation of the electron-proton mass hierarchy: invoking ’t Hooft’s chiral anomaly matching, unbroken chiral symmetry protects the composite D − D − D electron from confinement-scale mass, while the U − U − D proton acquires mass via strong non-Abelian topological curvature. In this picture the W ± mass scale (∼ 80.4 GeV) is interpreted as the topological activation energy Vyield for chiral inversion, with its explicit value providing a first calibration of the elastic constants of the matrix. Quantum superposition and wave-particle duality are described as the time-averaged statistics of localized soliton trajectories navigating an extended hydrodynamic phase field ψ = ReiS/ℏ. Pauli exclusion and Einsteinian gravity emerge as two scale-dependent limits of the same matrix elasticity: local divergent shear repulsion between identical knots and its coarse-grained continuum limit Gμν = 8πGTμν /c4.