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| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17183453 |
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Table of Contents:
- <p> </p> <p>### **Title**<br>Σ-Topological Theory of Emergence (TTE): A Unified Fractal-Topological Framework for Gravity, Mass, and Vacuum Structure — Supplemental Materials, Code, and Derivations</p> <p>### **Description**<br>This repository contains the supplemental materials for the manuscript "Σ-Topological Theory of Emergence (TTE)," which presents a unified framework where four-dimensional physics (gravity, particle masses, dark matter, and dark energy) emerges from the holographic projection of a stabilized 11-dimensional topological defect Σ embedded in a fractal quantum glass vacuum.</p> <p>**Core theoretical components include:**<br>* **Fractal Quantum Glass Vacuum:** Modeling the vacuum as a disordered ensemble of microscopic cells with a scale-dependent Hausdorff dimension.<br>* **Induced Gravity:** A heat-kernel derivation of the Einstein-Hilbert action from quantum fluctuations.<br>* **Topological FRG:** A Functional Renormalization Group (FRG) analysis incorporating topological corrections, yielding a vacuum suppression factor ε_d ≈ 0.15.<br>* **Geometric Mass Generation:** A Froggatt-Nielsen mechanism on Σ, generating fermion mass hierarchies via topological charges (m_i ∝ ε_d^q_i).<br>* **Falsifiable Predictions:** The framework yields specific, testable predictions, including an effective dimension D_eff ≈ 2.62 on 70-100 Mpc scales, a tensor-to-scalar ratio r ≈ 0.010, a sum of neutrino masses ∑m_ν ≈ 0.12 eV, gravitino mass m_3/2 ≈ 0.09 eV, gravitational-wave echoes, and a 21-cm spectral tilt α ≈ -2.48.</p> <p>**Repository Contents:**<br>* The complete manuscript PDF with detailed derivations.<br>* Explicit mathematical formulae and computational steps.<br>* Reproducible Python code (see Appendix E) for:<br> * Numerical integration of the FRG flow to obtain ε_d.<br> * Calculation of lepton masses using the Froggatt-Nielsen ansatz.<br>* Supplementary appendices providing technical details on heat-kernel coefficients, explicit FRG beta functions, a toy model for gravitational-wave echoes, sensitivity analysis, and Bayesian evidence calculations.</p> <p>This release aims to ensure full transparency, reproducibility, and to provide a foundation for further numerical and phenomenological development of the theory by the community.</p> <p>### **Keywords**<br>Quantum Gravity, Emergent Gravity, Fractal Universe, Topological Defects, Functional Renormalization Group (FRG), Froggatt-Nielsen Mechanism, Induced Gravity, Dark Matter, Dark Energy, Black Hole Information Paradox, Gravitational Wave Echoes, Falsifiable Predictions, Reproducible Research</p> <p>### **Authors**<br>Bolikov, Aleksandr</p> <p>### **Publication Date**<br>2025-09-23</p> <p> </p>