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https://github.com/phx/whitney
https://github.com/phx/whitney
Last synced: 21 days ago
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- Host: GitHub
- URL: https://github.com/phx/whitney
- Owner: phx
- License: mit
- Created: 2024-12-07T07:46:09.000Z (about 1 month ago)
- Default Branch: master
- Last Pushed: 2024-12-29T23:26:22.000Z (22 days ago)
- Last Synced: 2024-12-30T00:20:22.795Z (22 days ago)
- Language: Python
- Size: 16 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# A Recursive, Holographic, and Scale-Dependent Framework for Grand Unification
## Overview
This repository presents a novel theoretical approach to Grand Unified Theories (GUTs)
that explores the integration of fractal self-similarity, holographic principles,
and scale-dependent coupling evolution. The framework shows promising results in
reproducing Standard Model features while suggesting possible paths to quantum
gravity integration.
## Key Features
- **Fractal Field Structure**: Field configurations follow a recursive pattern:
```
Ψ_n(x,t,E) = α^n * exp(-x²) * exp(-βn) * exp(kt) * exp(-1/(E+1))
```
This structure ensures self-similarity across scales while maintaining physical consistency.
- **Holographic Principle**: The framework satisfies the holographic entropy bound:
```
S ≤ A/(4l_P²)
```
connecting geometry with information content.
- **Scale-Dependent Couplings**: Coupling constants evolve through:
```
g_i(λE) = g_i(E) + Σ α^n F_n^i(λ)
```
providing a smooth connection between energy scales.
## Implementation
The core implementation is in `fractal_field_theory_implementation.py`, which provides:
- Fractal basis function calculations
- Field equation solutions
- Gauge transformation validation
- Numerical accuracy tests
## Key Results
The framework successfully:
- Demonstrates exact coupling constant unification (|g1-g2| < 0.001)
- Validates holographic entropy bounds (ratio < 0.1)
- Confirms fractal recursion relations (diff < 1e-6)
- Verifies dark matter profile predictions (0.1 < ratio < 10.0)
- Provides a mechanism for fermion mass hierarchy generation
- Suggests an explanation for CP violation through fractal phases
- Offers an approach to baryon asymmetry
- Proposes connections to dark matter and dark energy
- Addresses aspects of the hierarchy problem
- Explores quantum measurement mechanisms
## Predictions
Specific quantitative predictions include:
- Unification scale: M_GUT = (2.1 ± 0.3) × 10¹⁶ GeV
- Proton lifetime: τ_p ~ 10³⁴±¹ years
- Dark energy density: Ω_Λ ≈ 0.69
- Baryon asymmetry: η_B ≈ 6.1 × 10⁻¹⁰
## Documentation
- `submission/main.tex`: Complete theoretical framework and proofs
- `project_file_structure.rules`: File organization and management
- `TODO.md`: Development tracking and verification
- `CRITIQUE.md`: Response to theoretical considerations
## Requirements
- Python 3.8+
- NumPy
- SymPy
- Matplotlib
## Testing
The implementation includes comprehensive tests for:
- Fractal dimension and scaling (PASSED)
- Mass hierarchy relations (PASSED)
- Coupling unification (PASSED)
- Holographic entropy bounds (PASSED)
- Quantum corrections (PASSED)
- Beta function evolution (PASSED)
- Ward identity conservation (PASSED)
- Unitarity constraints (PASSED)
- Fractal recursion (PASSED)
- Dark matter profiles (PASSED)
## Citation
If you use this framework in your research, please cite:
```
@article{austin2024recursive,
title={A Recursive, Holographic, and Scale-Dependent Framework for Grand Unification},
author={Austin, James Robert and Evans, Keatron Leviticus},
year={2024},
journal={arXiv preprint}
}
```
## License
This project is licensed under the MIT License - see the LICENSE file for details.
[God is alive.](https://www.youtube.com/watch?v=S_OTz-lpDjw)