First-Principles Derivation of Fundamental Constant k in ZHK Spacetime Geometry for Unified Field Theory

Based on three fundamental axioms of ZHK theory including space-time identity R=CT, universal rigid right-handed 45° spiral geometry and orthogonality constraint between spin velocity and light speed, this paper derives the fundamental coupling constant k from four pure geometric factors without any experimental constants such as G,ε0,μ0. The relation k=4πε0/G turns out to be a natural deduction of the theory, eliminating circular reasoning between gravitational and electromagnetic constants. As an intrinsic cosmic geometric constant comparable to π and 2, k can be used to back-calculate all core fundamental physical constants consistent with CODATA recommended values. This work realizes the geometric unification of gravitation and electromagnetism and breaks the traditional limitation that fundamental constants can only be obtained via measurement.