Geometric Derivation of the Hadronic Gravitational Coupling in Cl(3,0) from Boundary Phase Attenuation.

This paper presents a geometric derivation of the hadronic gravitational coupling constant within the Clifford algebra of three-space $\mathcal{C}\ell(3,0)$. Modeling the proton as a dynamic composite of three mutually precessing bivector sheets undergoing coupled Euler circulation, we establish dynamic orthogonality as an energetic ground state across an eighteen-dimensional configuration space. By evaluating boundary phase attenuation through the lightlike Compton horizon, we derive Newton’s gravitational constant as an attenuated electromagnetic phase leak: $G = \frac{\hbar c}{m_p^2}\sqrt{3}\left(1 - \frac{4\alpha}{3}\right)\alpha^{18} + \mathcal{O}(\alpha^2)$. This framework resolves the gauge hierarchy without free parameters and naturally accounts for the fourfold ratio between charge and Compton radii.