Gravity and Mass Hierarchy from Topological Solitons

Problem: The Standard Model describes particles as point-like objects, but point particles create singularities, require 19+ free parameters for masses, and cannot explain why gravity exists at all. General Relativity and quantum field theory remain incompatible at the Planck scale. Solution: We present a model in which particles are not points, but stable topological solitons - T2,3 torus knots - of a single elastic vacuum matrix.From the Faddeev-Skyrme Lagrangian we derive the fermion mass hierarchy, Pauli exclusion as topological shear repulsion, and emergent gravity as elastic matrix deformation. No point singularities, no extra dimensions, no exotic matter.The model is falsifiable. It predicts a finite soliton core radius Rc <= 2.0 x 10^-20 m and a confinement scale Lambda_c >= 10 TeV, derived from a single vacuum yield barrier V_yield ~ 80.4 GeV (m_W). If a point-like electron is found below this scale, or if no soliton substructure appears at Lambda_c, the model is ruled out. Part 2 of the Kramer Trilogy 2026. Companion to A Necessary Descent from Nothing (https://doi.org/10.5281/zenodo.24147063) and Cyclic Cosmology from Vacuum Relaxation (https://doi.org/10.5281/zenodo.24147124). Author: Cornelis Kramer, Rotterdam, The Netherlands. ORCID: 0009-0009-9485-2485.