7.6 Spectral Unification of Coupling Constants

Abstract

This paper proves that the running indices of the four coupling constants — electromagnetic, weak, strong, and gravitational — are uniformly determined by the Jacobian eigenspectrum of the Birkhoff Mixing Matrix . The eigenvalues of the Hessian matrix of the Algebraic Action at the fixed point couple with the Birkhoff eigenvalues, yielding a unified running framework for the four couplings. At the Grand Unification scale, complete constraint release causes all four couplings to converge to the same geometric value . This paper provides the complete computation of the Hessian eigenvalues, the determination of the projection weights for the running indices, and the geometric derivation of the Grand Unification value .