Why the Hydrogen Atom Is This Size: The Bohr Radius from Electron Field Extension

The Bohr radius a₀ = 52.9 pm is conventionally derived as ℏ/(mₑcα), with no structural explanation for why the hydrogen atom is this particular size. We show that the Bohr radius is the free electron's coherent field — 83,733 lattice units ≈ 4.4 pm, derived from the g−2 harmonic structure — deployed across V = 12 vertex positions of the icosahedral lattice. The predicted radius is 83,733 × 12 × 0.0521 fm = 52.4 pm, matching the measured 52.9 pm to 1.1%. This identifies the Bohr radius as a two-body quantity: not a property of the electron alone, but the electron's self-interaction field extended to comply with the proton's twelve-vertex geometry. The growth factor V = 12 connects two previously separate derivations in the Bootstrap Universe framework: the free electron (described by the g−2 harmonic series) and the bonded electron (described by the hydrogen binding energy expansion). The Rydberg energy E₀ = (α⁻¹ − 1)/(V − χ) is the energy cost of this compliance, distributed across V − χ = 10 effective vertices. The three golden rectangles of the icosahedron — each containing 4 of the 12 vertices — provide the angular structure (p-orbitals); V = 12 provides the radial scale.