What question did this study set out to answer?

This research aims to show how the non-trivial zeros of the Riemann zeta function relate to fundamental physical laws.

March 26, 2026Open Access

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

Key Points

This research aims to show how the non-trivial zeros of the Riemann zeta function relate to fundamental physical laws.
Explored the KIT framework in relation to particle masses and fundamental constants.
Established convergence results linking spectral stiffness to the Gaussian normalization constant.
Examined the relationship between space, time, and Riemann zeros to explain physical invariance.
Showed that the KIT particle mass spectrum converges to the Gaussian normalization constant.
Established that space and time are conjugate partners relating to the Riemann zeros.
Unified gravity and electromagnetism through a common origin based on Riemann zeros.

Abstract

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.

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