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…