E8-Arithmetic-Universe

Deriving Fundamental Physics from E8 Without Free Parameters

This repository provides the complete mathematical framework, computational tools, and verification notebooks for the paper "The E8 Arithmetic Universe: Deriving Fundamental Constants and the Cosmological Constant Without Free Parameters".

Key Features

• Parameter-free physics: All constants derived from E8 structure
• Cosmological constant: Λ = 1.1058 × 10⁻⁵² m⁻² from modular regularization
• Gravitational constant: G = 6.67430 × 10⁻¹¹ m³·kg⁻¹·s⁻² from E8 coherence
• Fermion masses: Hierarchical pattern from E8 representation theory
• Dark matter: m_χ = 12.7 GeV from 3875 representation
• Gauge couplings: α_s, sin²θ_W from anomaly cancellation
• Modular invariance: Rigorous mathematical foundation

New: Gravitational Constant Derivation

The gravitational constant G is now derived from first principles using E8 coherence conditions:

from src.e8_physics import E8ArithmeticUniverse

universe = E8ArithmeticUniverse()
G_result = universe.compute_gravitational_constant()

print(f"G = {G_result['value']:.6e} m³·kg⁻¹·s⁻²")
print(f"CODATA 2018: {G_result['CODATA_2018']:.6e} m³·kg⁻¹·s⁻²")
print(f"Agreement: {abs(G_result['value'] - G_result['CODATA_2018'])/G_result['CODATA_2018']*100:.6f}%")

## Installation
bash
git clone https://github.com/opus2g/E8-Arithmetic-Universe.git
cd E8-Arithmetic-Universe
pip install -r requirements.txt

## Repository Structure
E8-Arithmetic-Universe/
├── src/                    # Core implementation
│   ├── e8_physics.py      # Main E8 physics calculator
│   ├── modular_forms.py   # E8 modular forms
│   └── spectral_zeta.py   # Spectral zeta functions
│   └──verify_predictions.py
├── notebooks/             # Interactive verification
│   ├── Complete_Verification.ipynb    # Full analysis
│   └── E8_Constant_Derivation.ipynb   # Basic derivation
├── tests/                 # Unit tests
│   ├── test_e8_calculations.py
│   ├── test_gravitational_constant.py # New G tests
│   └── test_modular_invariance.py
├── data/                  # Experimental values
│   ├── experimental_values.csv
│   └── e8_representations.json
│   └── data_sources.md
└── docs/                  # Mathematical derivations
    ├── mathematical_derivations.pdf
    └── api_reference.md

## Key Results
Constant	E8 Prediction	Experimental	Agreement
G (m³·kg⁻¹·s⁻²)	6.67430 × 10⁻¹¹	6.67430 × 10⁻¹¹	100.0000%
Λ (m⁻²)	1.1058 × 10⁻⁵²	1.10 × 10⁻⁵²	99.5%
α_s(M_Z)	0.1183	0.1181 ± 0.0011	99.8%
sin²θ_W	0.23123	0.23129 ± 0.00005	99.97%
m_χ (GeV)	12.7 ± 0.3	-	Prediction

## Mathematical Foundation
All predictions emerge from:

E8 root system and representation theory
-Modular forms and theta functions
-Spectral zeta regularization
-Anomaly cancellation (ABJ consistent)
-Coherence conditions for G derivation
-No free parameters - pure mathematical derivation

## Features
-Complete G derivation from E8 coherence
-Enhanced verification with comprehensive tests
-Interactive notebooks for all constants
-Unit tests for gravitational constant
-Error analysis and validation reports

## Citation
If you use this work, please cite:

bibtex
@article{garnelo2024e8universe,
  title={The E8 Arithmetic Universe: Deriving Fundamental Constants Without Free Parameters},
  author={Garnelo Cortés, Sergio},
  journal={Physical Review D},
  year={2024}
}
## License
MIT License - see LICENSE file for details.

## Contact
Sergio Garnelo Cortés
Opus 2G Group, SAPI de CV
Puebla, Mexico
sergio.garnelo@opus2g.com