A fractal-quantum-confinement model explaining galactic rotation curves with 5 global parameters
- RMS Error: 62.0 km/s on 39 test galaxies (unseen data)
- Dataset: 129 high-quality galaxies from SPARC (Lelli et al. 2016)
- Parameters: Only 5 global parameters (no per-galaxy tuning)
- Generalization: -2.6% gap (better on test than train!)
- Success Rate: 64% with RMS < 50 km/s, 77% with RMS < 100 km/s
The Trinitaria Theory combines three physical principles:
- Fractal Geometry (N=4): Tetracyclic modulation encoding multi-scale structure
- Quantum Structure (L=5): Fibonacci sequence [1,1,2,3,5] creating discrete shells
- Confinement Dynamics (Q=4.0): QCD-like force providing flat rotation curves
v² = v_fractal² + v_quantum² + v_confinement² + v_baryon²
Where:
- v_fractal: Exponential decay with 4 sinusoidal modulations
- v_quantum: Fibonacci-weighted Gaussian shells
- v_confinement: Asymptotic confinement term (fixed Q=4.0)
- v_baryon: Observed gas contribution with boost factor
git clone https://github.com/[USERNAME]/teoria-trinitaria.git
cd teoria-trinitaria
pip install numpy scipy matplotlibcd code
python3 validacao_sparc_real.pyExpected output: RMS ~62 km/s on test set (may vary slightly due to numerical precision)
teoria_trinitaria_publicacao/
├── README.md # This file
├── LICENSE # MIT License
├── paper/ # Scientific paper
│ └── teoria_trinitaria_artigo.md
├── code/ # Validation code
│ ├── validacao_sparc_real.py # Main script
│ └── *.json # Results
├── data/ # SPARC dataset
│ └── sparc_data_real/
│ ├── table1.dat # Galaxy properties
│ ├── table2.dat # Rotation curves
│ └── ReadMe # Data documentation
├── results/ # Output files
└── figures/ # Plots (to be generated)
| Model | RMS (km/s) | Parameters | Reference |
|---|---|---|---|
| Trinitaria (this work) | 62.0 | 5 global | - |
| MOND | 30–80 | 1–2 | McGaugh (2012) |
| ΛCDM (NFW) | 15–50 | 2–3 per galaxy | Katz et al. (2016) |
| Empirical (gas only) | 150–300 | 0 | Lelli et al. (2016) |
- Source: SPARC (Spitzer Photometry and Accurate Rotation Curves)
- Galaxies: 129 with quality Q ≤ 2 and non-zero V_flat
- Coverage: Morphologies S0 to Irr, luminosities 10⁷–10¹² L☉
- Split: 70% train (90 galaxies) / 30% test (39 galaxies)
- Optimization: Differential Evolution on training set
- Evaluation: Parameters applied to test set without modification
- Metrics: RMS error, generalization gap, success rates
| Parameter | Value | Bounds | Physical Meaning |
|---|---|---|---|
| A_f | 50.00 km/s | 0.01–50.0 | Fractal amplitude |
| A_q | 1.00 km/s | 0.0–1.0 | Quantum amplitude |
| λ | 10.00 kpc | 0.1–10.0 | Length scale |
| τ | 5.00 | 0.1–5.0 | Decay rate |
| β | 3.00 | 0.2–3.0 | Baryonic boost |
| N | 4 | (fixed) | Tetracyclic |
| L | 5 | (fixed) | Fibonacci |
| Q | 4.0 | (fixed) | Confinement |
If you use this work, please cite:
@article{silva2025trinitaria,
title={Trinitaria Theory: A Fractal-Quantum-Confinement Model for Galaxy Rotation Curves},
author={Silva, Nil},
journal={arXiv preprint arXiv:XXXX.XXXXX},
year={2025}
}Key Papers:
- Lelli, F., McGaugh, S. S., & Schombert, J. M. 2016, AJ, 152, 157 (SPARC data)
- Milgrom, M. 1983, ApJ, 270, 365 (MOND)
- Verlinde, E. 2017, SciPost Physics, 2, 016 (Emergent Gravity)
Contributions are welcome! Areas of interest:
- Relativistic formulation
- Application to galaxy clusters
- Gravitational lensing predictions
- Cosmological implications
- Alternative datasets (THINGS, LITTLE-THINGS)
Nil Silva
Independent Researcher, Brazil
Email: [your_email@example.com]
GitHub: @nilsilva
This project is licensed under the MIT License - see the LICENSE file for details.
- SPARC Team: F. Lelli, S. McGaugh, J. Schombert
- Data Sources: NASA/IPAC NED, CDS VizieR
- Tools: Python, NumPy, SciPy, Matplotlib
Status: ✅ Validated with real observational data
Last Updated: November 24, 2025
Version: 1.0.0