Topological Origin of Interaction Hierarchy in Elastic Vacuum (World Crystal)

This paper proposes a geometric solution to the hierarchy problem of fundamental interactions based on the World Crystal model with topological defects. The vacuum is postulated as an elastic incompressible 3D-hypersurface (Cosserat membrane) with an effective thickness h ~ ℓP and Poisson's ratio ν = 0.5. Relying on the gauge theory of defects (H. Kleinert), an isomorphism is established: dislocations generate torsion fields (electromagnetism), while disclinations generate curvature (gravity). Applying the theory of elasticity for thin plates (Föppl–von Kármán approximation) demonstrates a fundamental difference in field scaling: dislocation energy (charge) is determined by membrane stiffness (~ h), whereas disclination energy (mass) is determined by bending stiffness (~ h³). The geometric suppression factor ξ ~ (h/L)², where L is the Compton wavelength, naturally reproduces the observed hierarchy of coupling constants G/ke ~ 10⁻⁴⁰ without invoking fine-tuning hypotheses.