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

This paper presents a deterministic, bottom-up topological field framework for the emergence of the spacetime metric, gauge charges, and invariant rest mass from an absolute vacuum state. While standard cosmological models and gauge field theories rely on unintegrated vacuum singularities, ad-hoc fine-tuning, and empirical Yukawa parameters, this framework formulates structural transitions across recursive scale regimes, culminating in the subnucleonic Planck-boundary regime of our present epoch, driven by exponential topological bifurcation. Throughout all evolutionary phases, net field charge is strictly conserved via the conjugate balance of centripetal field contraction and kinetic-dispersive expansion. We demonstrate how fundamental fermions emerge as quantized 3D topological solitons (Hopfions), governed by the non-linear mechanics of the Faddeev-Skyrme Lagrangian. The electron-proton mass hierarchy is resolved at subnucleonic confinement scales by invoking 't Hooft's Chiral Anomaly Matching condition: unbroken chiral symmetry dynamically protects the composite electron from acquiring confinement-scale mass, whereas strong non-Abelian topological curvature in the proton induces spontaneous chiral symmetry breaking. Furthermore, the massive W gauge bosons of the weak interaction are reinterpreted not as fundamental particles, but as the topological activation energy (yield threshold) required for chiral inversion during topological phase transitions such as beta decay. Addressing the measurement problem, this framework mathematically decouples the wavefunction into real structural amplitude and hydrodynamic phase, reinterpreting quantum superposition and wave-particle duality not as intrinsic ontological uncertainties, but as the time-averaged statistical representation of deterministic, highly localized sub-particle trajectories navigating an extended hydrodynamic topological wake. Finally, the Pauli Exclusion Principle and Einsteinian gravity are natively unified: quantum exclusion emerges locally as classical geometric shear repulsion between identical topological knots, which mathematically integrates via continuous coarse-graining into the macroscopic pseudo-Riemannian metric curvature of General Relativity.