Title: The Gravitational Constant from Soliton Topology Author: Alexander Novickis (alex.novickis@gmail.com) We derive Newton's gravitational constant $G$ from the fine structure constant $\alpha$ and the electron mass $m_e$ within the topological soliton framework. The natural form $G = \alpha^{21 - (15/2)\alpha}\hbar c/m_e^2$ achieves 0.015% accuracy with no rational prefactor; the further-corrected $G = \alpha^{21-(15/2)\alpha-\gamma\alpha^2}\hbar c/m_e^2$ (Euler-Mascheroni 2-loop) achieves $4.5 \times 10^{-6}$%; the rational-prefactor form $G = (17/13)\alpha^{21}\hbar c/m_e^2$ (0.12%) is the rational-fit approximation to $\alpha^{-(15/2)\alpha}$ at $\alpha \approx 1/137$. The conformal-group $SO(4,2)$ one-loop running with 15 generators is the structural origin of the formerly-rational prefactor. By the same logic (b50), the proton mass is also derived: $m_p = m_e\,\alpha^{-3/2 - (15/4)\alpha}$ (0.055% PDG), where the half-power $-(15/4)\alpha$ correction reflects mass = $\sqrt{\rm mass^2}$. The earlier compact form $m_p = \sqrt{17/13}\,m_e\,\alpha^{-3/2}$ was the rational-fit equivalent, now superseded; $\sqrt{17/13}$ approximates $\alpha^{-(15/4)\alpha}$. The Planck/proton-mass identity $m_p \cdot M_P = m_e^2 \cdot \alpha^{-12}$ is exact: the running corrections cancel between the two masses. The hierarchy problem — gravity is $10^{45}$ times weaker than electromagnetism — reduces to $\alpha$ raised to a Hopf-tower exponent. The same democratic normalisation yields $\alpha_s = \alpha^{13/30} = 0.1186$ (0.5% from measured), where 13 visible DOF ($M_4 + S^3 + F_2$) out of 30 total set the ratio. The 30 = 13 + 17 split connects $\sin^2\theta_W = 3/13$ (Weinberg angle), $\alpha_s$, and the quark mass denominator $D = 17$ (Paper LXV) through one partition of internal DOF. Combined with $\rho_\Lambda \sim \alpha^{16}m_e^4$ (Paper XI), this completes the link between all fundamental scales and couplings from a single dimensionless constant $\alpha$. Keywords: gravity, hierarchy problem, fine structure constant, Planck mass, proton mass, conformal group, SO(4,2), running coupling, Kaluza Klein, soliton, strong coupling, alpha s, Schur's lemma, democratic normalisation DOI: 10.5281/zenodo.19349143 Series: Paper LXVIII in the Hopf Soliton Programme