Kochenov_Geometric_Identity_for_G

This work reports a purely geometric expression for the Newtonian gravitational constant G using only the golden ratio φ, the integer 31, and √5. No CODATA values, no fitted parameters, and no experimental input are used in the derivation. The main identity is: G \times 10^{11} = \frac{31^2 \times \sqrt{5}}{\phi^{12}} The resulting value G_{Koch} = 6.67354674496\ldots \times 10^{-11} lies between the Schlamminger (2014) and CODATA 2018 measurements. Its deviation from each is smaller than the mutual disagreement between the two experiments. A supporting generator identity is given: \frac{\phi^{12}}{\sqrt{5}} = 144 + \frac{1}{720} + \mathcal{O}(10^{-8}) where 720 = 6! and 144 = F12 (the only perfect square in the Fibonacci sequence). The residual 1/720 further appears independently in the neutron–proton mass ratio and in the electromagnetic fine‑structure constant, suggesting a common geometric origin. The number 31 = 2⁵ − 1 (a Mersenne prime, maximally saturated 5‑bit binary) serves as a structural anchor. The scaling block S = \phi^6 \times 31 \approx 556.27 defines the spiral step; four turns of this block reproduce the 10¹¹ factor. No dynamical model is claimed. The document presents a numerical observation, fully reproducible from the given formulas. Author: Boris V. Kochenov Contact: [email protected] Date: April 2026 License: CC BY 4.0 (or as you prefer)