Geometric Derivation of Proton Radius Matches Codata Within 577 Ppm

  GEOMETRIC BASIS:
  1^2 + 2^2 = (sqrt(5))^2
  w = 2 (Structural Constant)
  δ = sqrt(5) (Dynamic Constant)

  GRAVITATIONAL HIERARCHY:
  r_p ≈ w * (m_P / m_p)^2 * r_s
  r_p = w^2 * (ħ / (m_p * c))
  r_p = w^2 * ƛ_p
  r_p ≈ 8.41235 x 10^-16 m
  
  Experimental: 8.4075 (64) x 10^-16 m [CODATA 2022]
  Discrepancy: 577 ppm

  PROTON MAGNETIC MOMENT:
  g_p = (δ^2 / w) * δ
  g_p = 2.5 * sqrt(5) ≈ 5.590
  
  Experimental: 5.58569 [CODATA 2022]
  Discrepancy: 802 ppm

  NEUTRON-PROTON MASS GAP:
  ∆m = m_e * ((δ^2 / w) + w^2 * α)
  ∆m ≈ 1.29241 MeV
  
  Experimental: 1.29333 MeV
  Discrepancy: 711 ppm

  COSMOLOGICAL RATIO:
  Ω_Λ / Ω_m = δ
  Ω_Λ / Ω_m = 2.2360
  
  Experimental: 2.2144 [Planck 2018]
  Discrepancy: < 1%

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  TOPOLOGICAL ORIGIN:
  In a D = 3 universe, Mass scales as Volume (L^3):
  
  Linear scaling (r): r ~ m^(1/3)
  Surface scaling (A): A ~ r^2 ~ m^(2/3)

  w = (Surface exp) / (Linear exp) = (2/3) / (1/3) = 2
  
  NULL HYPOTHESIS CHECK:
  If D != 3  =>  w != 2  =>  Predictions fail.
  Empirical data validates D = 3 topology.