Derives Newton's gravitational constant G from proton properties using a 216-vertex twin construction with a D₄ bridge. The closed-form relation matches experimental values to 5.6 × 10⁻⁴ accuracy.
The paper derives Newton's gravitational constant G from proton properties using a 216-vertex twin construction with a D₄ bridge. The closed-form relation G = α^(1/8) × (12/7) × ℏc/mₚ² matches experimental values to 5.6 × 10⁻⁴ accuracy. A symmetric integer matrix Laplacian produces 23 eigenvalues, with 54% at exact integers. Four eigenvalue-multiplicity pairs align with established Pentagon Physics quantities. The work presents general relativity as the continuum equation of this operator, with lower eigenvalues corresponding to matter and higher ones to regimes where standard GR predicts singularities. Five falsification conditions are stated explicitly, and supplementary materials include Python code and a spreadsheet with the full spectrum and vertex coordinates.