The Gravitational Constant from FCC Void Geometry

We derive Newton’s gravitational constant G from first principles using the Face-Centered Cubic (FCC) void geometry established in Etheron Volume 3. We propose that the hierarchy between electromagnetic and gravitational couplings is determined by the ratio of surface dynamics to bulk phase space modes, scaling as φn . The exponent is derived as n = Dpos × Dst × (Dst ! − Dphase ) − Ωv /Dst ≈ 203.935. All parameters emerge naturally from the dimensional structure √ of the vacuum: Dpos = 3, Dst = 4, Dphase = 7, and the FCC void fraction Ωv = 1 − π/(3 2). The formula predicts G to within 0.06% of the CODATA 2018 value with zero free parameters. Furthermore, we demonstrate that the Schwarzschild metric arises from void density compression and predict a geometric correction to Bekenstein-Hawking entropy of 3.7%, offering a falsifiable test for the theory.