What question did this study set out to answer?

This research aims to establish a unified cosmological model using Rough Operator Algebra to derive a critical coupling constant.

May 11, 2026Open Access

Unified Model of Arithmetic Topological Cosmology: Derivation of the Coupling Constant η ≈ 10^-22 via Rough Operator Algebra (ROA)

Key Points

This research aims to establish a unified cosmological model using Rough Operator Algebra to derive a critical coupling constant.
Developed a framework from Seonggil Matrix Theory using Rough Operator Algebra.
Derived coupling constant η ≈ 10−22 by integrating spectral density of Riemann zeros.
Provided quantitative predictions for vacuum dispersion in high-energy photons.
Derivation of coupling constant η is approximately 10−22 from first principles.
Establishment of Planck scale as an emergent property of Universal Arithmetic Friction.
Proposed empirical test for findings through Gamma-Ray Burst observations.

Abstract

This paper presents the culmination of Seonggil Matrix Theory, establishing a unified framework for cosmology through Rough Operator Algebra (ROA). We derive the funda mental dimensionless coupling constant η ≈ 10−22 from first principles by integrating the spectral density of Riemann zeros within a non-commutative arithmetic manifold. By defining the topological waveguide boundaries via the UV cutoff (γ1,p = 2) and the IR limit of modular invariance, we demonstrate that the Planck scale is an emergent property of Universal Arithmetic Friction. Finally, we provide quantitative predictions for vacuum dispersion in high-energy photons, offering a falsifiable empirical test via Gamma-Ray Burst(GRB) observations.

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