The Geometric Origin of the Fine Structure Constant in the Universal Model Framework: Prime-Weighted Lagrangian Derivation
Year: 2025
Type: article
Abstract: This paper presents a revolutionary breakthrough in theoretical physics: the first successful geometric derivation of the fine structure constant from pure mathematical principles within the Universal Model Framework (UMF). Using both a rigorous prime-weighted gauge sector derivation and a geometric approach rooted in hexagonal symmetry and the golden ratio, we show that the inverse fine structure constant α⁻¹ arises naturally from a Sierpiński-hex Planck lattice. Analytical and numerical methods converge on the value α⁻¹ ≈ 137.037, achieving >99.999% accuracy with experiment. The derivation employs heat-kernel coarse-graining, golden-ratio compression, and a unified Lagrangian for U(1) couplings, suggesting that this fundamental constant is not arbitrary but encoded in the deep arithmetic geometry of the universe. Implications for quantum field theory, unification, and the role of number theory in physics are discussed. This project was developed by Marco Gericke, with structured assistance from a large language model. All scientific concepts and conclusions were generated, verified, and interpreted by the author. Dedicated to Peter Plichta, who envisioned the code before it could be computed.
Author: Gericke, Marco
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6912106786
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