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Why Gravity is Weak and Why There is a Hierarchy: The Gravitational Coupling from S² Compact Geometry and Resolution of the Hierarchy Problem from Trit Winding Numbers

Authors: Douzenis, Apostolos;

Why Gravity is Weak and Why There is a Hierarchy: The Gravitational Coupling from S² Compact Geometry and Resolution of the Hierarchy Problem from Trit Winding Numbers

Abstract

Two of the deepest puzzles in theoretical physics are: (i) why gravity is 10⁴³ times weaker than electromagnetism for the electron, and (ii) why the Higgs boson mass (125 GeV) is 10¹⁷ times smaller than the Planck mass, apparently requiring extreme fine-tuning. This paper resolves both from the Trit compact phase framework [1–4]. The gravitational coupling is proportional to mass (rather than constant like electric charge) because the graviton compact phase lives on S² (spin-2) rather than S¹ (spin-1): the spin-2 polarisation tensor ε_{μν} contracts with the energy-momentum tensor T_{μν} ∝ m, making the coupling inherently mass-proportional. The ratio of gravitational to electromagnetic force between two electrons is F_grav/F_EM = (m_e/m_P)²/α = 2.407×10^{-43}, where m_e, m_P, and α are all independently derived Trit predictions. The measured ratio is 2.40×10^{-43} (+0.3%). The hierarchy between the Higgs mass and the Planck scale is not fine-tuning: it is the gap Δx = x_H - x_P = 7.95 between the Higgs winding number (x_H = 35.46, derived from g_{Trit} × √2 × m_t) and the Planck winding number (x_P = 27.51). Both are derived; no cancellation is needed. The ratio m_H/m_P = α^{7.95} = 1.033×10^{-17} agrees with the observed m_H/m_P = 1.024×10^{-17} to 0.9 percent.

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