A formula for Newton's gravitational constant from the f ine-structure constant, motivated by Kaluza–Klein reduction on S2

A phenomenological formula for Newton's gravitational constant G in terms of the fine-structure constant alpha, motivated by six-dimensional Kaluza-Klein reduction on S^2. The formula G = (phi^2/2)(1 + 3*alpha^2 + (phi/2)alpha^3) * alpha^21 * hbarc/m_e^2 predicts G = 6.674298 x 10^-11 m^3 kg^-1 s^-2, deviating from the CODATA 2018 value by -0.31 ppm (-0.33 ppm for CODATA 2022) with zero parameters fitted to G. The leading order (Brans-Dicke parameter omega=0, bridge exponent dD-3=21) follows from standard KK reduction. The bridge coefficient phi^2/2 comes from a vacuum polynomial ansatz. The correction coefficients c_2=3 and c_3=phi/2 are geometrically identified but not yet derived from first principles. The dimensionality d=4, D=6 is selected by three constraints. Accompanying open-source computational framework (2130 unit tests, 45 modules): https://github.com/rdnjm/Alpha-Ladder Interactive dashboard: https://alphaladder.streamlit.app/