KIT Spectral Stiffness Sum: Convergence to the Gaussian Normalization Constant, the Gravitational Scale Parameter, and the Space Time Conjugate Structure

This paper demonstrates that the non-trivial zeros of the Riemann zeta function are not merely mathematical curiosities but fundamental frequencies of physical law. Within Kim’s Isotropic Template (KIT) framework, the spectral stiffness factors ∣ζ′(ρn)∣2 reproduce particle masses, Newton’s gravitational constant, and the invariance of the speed of light — all with zero free parameters. We establish two convergence results: (i) S(n)/n17/10→1/2π, linking the KIT particle mass spectrum to the Gaussian normalization constant of the Stochastic Planck Time Hypothesis (SPTH); and (ii) tanh⁡(S(n)/K)→1 with K=88.38, coinciding with the KIT derivation of the gravitational constant. Furthermore, space and time are identified as conjugate Riemann zero partners, from which the invariance of c, the Minkowski metric signature, and Lorentz transformations follow geometrically without additional postulates. This work provides the first geometric explanation of Einstein’s postulate of light-speed invariance and unifies gravity and electromagnetism through the same Riemann zero origin.