Topological Vacuum Structure and the Geometric Origin of Fundamental Couplings: A Riemann-Cartan Approach
Iván Ugidos Martínez (espejogalactico@gmail.com)
v1.1 — July 9, 2026 Version 1.1 — Revised manuscript addressing reviewer feedback on dimensional analysis, symmetry breaking scales, and mass hierarchy predictions.
10.5281/zenodo.21268209
The Standard Model of particle physics successfully describes fundamental interactions but leaves the origin of its dimensionless parameters as empirical inputs. In this paper, we propose a rigorous topological reformulation of the quantum vacuum, modeling it as a Riemann-Cartan manifold endowed with non-vanishing torsion and a spontaneously broken discrete icosahedral substructure at the Planck scale. We provide a topological estimation of the fine-structure constant α and show that electric charge quantization emerges naturally from the icosahedral order parameter space. Furthermore, we identify a topological correction to the muon anomalous magnetic moment, explicitly recognizing a hierarchy problem analogous to the Higgs hierarchy. We conclude by proposing falsifiable predictions for high-energy astrophysics and an exploratory hypothesis for macroscopic negentropic cooling.
- Clarification of symmetry breaking:
$I_h \subset SO(3) \subset SO(1,3)$ . - Honest assessment of the 34 orders of magnitude scale hierarchy problem in the muon g-2 prediction.
- Explicit comparison of topological mass baselines (4:9:25) with experimental lepton masses (1:207:3477).
- Isolation of the GEM-01 macroscopic cooling protocol as an exploratory hypothesis.
- Addition of Section 7: Open Problems and Future Directions.
GEM_Topological_Vacuum_Structure_v1.1.pdf(The compiled 21-page paper)main.tex(Master document)01_Introduction.texto07_Open_Problems.tex(Section source files)README.md(This file)LICENSE.txt(CC BY-SA 4.0)
Copyright (c) 2026 Iván Ugidos Martínez. This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).
If you use this work in your research, please cite as:
Ugidos Martínez, I. (2026). Topological Vacuum Structure and the Geometric Origin of Fundamental Couplings: A Riemann-Cartan Approach (v1.1). Zenodo. https://doi.org/10.5281/zenodo.21268209
The authors acknowledge the foundational work of Élie Cartan, Emmy Noether, and the Einstein-Cartan theory community. This research builds upon decades of theoretical physics exploring the geometric structure of spacetime.
For questions, collaborations, or experimental validation proposals, please contact: espejogalactico@gmail.com