Deriving the Gravitational Constant from Electromagnetic Coupling and Three-Phase Geometry

The gravitational constant G is derived from the electromagnetic fine structure constant α, the proton mass, and the geometric structure of three-phase wave interference. The formula G = √3 · α¹⁸ · ℏc/m²_p reproduces the measured value to 0.99% with zero adjustable parameters. The factor √3 is the amplitude amplification at a three-phase convergence point. The exponent 18 is derived rigorously from group theory: the gravitational interaction must be invariant under the full symmetry group Z₃ × Z₃ × Z₂ of two three-mode convergences coupled through a chiral channel, and the order of this group is 3 × 3 × 2 = 18. Each group element contributes one factor of α, yielding α¹⁸. The formula is verified against twelve independent gravitational measurements — all consistent within 1.4%. The predicted G = 6.740 × 10⁻¹¹ matches Cavendish's original 1798 measurement exactly. A complete mass chain follows: the proton mass is the Planck mass times 3¹ᐟ⁴ · α⁹ (0.5%), the pion mass is m_p × 4/27 through two DST projections (0.4%), and the proton radius is 4ℏ/(m_p·c) (0.05%). The entire mass hierarchy from the Planck scale to the pion — spanning 17 orders of magnitude — is connected by powers of α, factors of 3, and the projection ratio 2/3. Two measured inputs (α and one mass) determine everything. The hierarchy problem dissolves: the 10³⁶ ratio between electromagnetic and gravitational strength is α⁻¹⁷/√3, a geometric identity rather than a fine-tuning puzzle.