Emergence of Spacetime and Mass Hierarchy via 3D Topological Solitons

We present a deterministic, unified topological field framework that resolves the fundamentalincompatibility between Quantum Mechanics and General Relativity. Departingfrom the standard paradigm of isolated point-particles propagating through a passive void,we demonstrate that spacetime geometry, gauge charges, and invariant rest mass emergefrom the continuous elastic dynamics of a single vacuum matrix. Within this strict topological monism, fundamental fermions are modeled as quantized3D topological solitons (Hopfions, T2,3 torus knots) of the Faddeev-Skyrme Lagrangian. Thisgeometry natively resolves the Standard Model mass hierarchy: invoking ’t Hooft’s chiralanomaly matching, the purely Abelian D − D − D electron is topologically protected fromconfinement-scale mass, while the non-Abelian U − D − U proton acquires heavy invariantmass via spontaneous symmetry breaking. Furthermore, the W± boson mass scale (∼ 80.4GeV) is successfully reinterpreted as the exact topological activation energy (Vyield) requiredfor chiral inversion. Crucially, this framework redefines quantum superposition and wave-particle dualitynot as irreducible probabilistic phenomena, but as the time-averaged statistics of localizedsoliton trajectories navigating deterministic hydrodynamic phase fields. At the macroscopicscale, Einsteinian gravity and the Pauli exclusion principle are unified natively as two scaledependentlimits of the exact same matrix elasticity: local divergent shear repulsion betweenidentical knots, and its coarse-grained pseudo-Riemannian continuum limit.