The Bridge from Spacetime Lattice to Atomic Scale: Proton Mass, Bohr Radius, and the Tension Fairy

The Bootstrap Universe framework derives a spacetime lattice spacing a = 0.053 fm from the axiom I AM I. The Bohr radius of hydrogen is a₀ = 52,918 fm — a factor of 10⁶ larger. This paper closes the gap. We show that the hydrogen atom, reconstructed on the Bootstrap lattice, yields the exact bridge formula a₀/a = (V/D) × μ × α⁻¹, where every factor is either axiomatic or previously derived: V/D = 4 (icosahedral vertices per dimension), μ = 6π⁵ (proton-electron mass ratio), and α⁻¹ = 137.036 (fine structure constant). The bridge implies E_L/m_p = V/D = 4 at zeroth order, which we refine to the proton mass formula m_p = (E_L/4)[1 + D²α/(D²−1) × (1 − ε/d)], accurate to 0.09 ppm (87 eV) with zero free parameters.…