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 S². The formula G = (phi²/2) (1 + 3*alpha² + (phi/2) alpha³) * alpha²1 * hbarc/mₑ² predicts G = 6. 674298 x 10^-11 m³ 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 phi²/2 comes from a vacuum polynomial ansatz. The correction coefficients c₂=3 and c₃=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/