Two-Tier Steady-State Cosmology and the Discovery of a Universal Scaling Law
A unified theoretical framework explaining galactic rotation curves without invoking particle dark matter, reconceptualizing the universe as a Two-Tier System where gravity emerges from information transport and interface energy.
Analysis of the complete SPARC database demonstrates a clear bimodal distribution:
| Phase | Criterion | Count | Percentage |
|---|---|---|---|
| Order (Stable) | M < 0.5 | 133 | 78.2% |
| Chaos (Unstable) | M ≥ 0.5 | 37 | 21.8% |
The sharp concentration near M ≈ 0 demonstrates that the majority of galaxies have achieved thermodynamic equilibrium with Tier 2 (Cosmic Web).
Figure 2: Distribution of QIC-S Phase Metric M for 170 SPARC galaxies. Order Phase (blue): 78.2%, Chaos Phase (red): 21.8%.
We discover a single power law spanning four orders of magnitude from galactic scales (~10 kpc) to cosmic large-scale structures (15 Mpc):
Figure 3: Universal scaling of Hamiltonian dynamics from galaxies to filaments. SPARC galaxies (N=170) and Cosmic Web filaments align on a single power law.
Bootstrap Validation (N = 10,000 resamples):
- Scaling exponent: α = 1.40 ± 0.10
- 95% CI: [1.24, 1.59]
- Strictly excludes trivial kinematic scaling (α = 1.0)
Figure 4: Statistical validation via bootstrap resampling. The 95% CI strictly excludes α = 1.0.
This constitutes definitive evidence that galaxies and Cosmic Web filaments belong to the same universality class.
Figure 1: Representative Order Phase galaxy NGC 0100. Upper: rotation curve with QIC-S prediction. Lower: Hamiltonian Landscape visualization (M = 0.164).
Tier 1: Regenerative Cosmology
- Galactic scale: Birth → Growth → Death → Rebirth
- Time: A locally emergent phenomenon
- Six-phase galactic lifecycle
Tier 2: New Steady-State Cosmology
- Cosmic scale: Stationary (Eternal Present)
- Angular momentum circulation via Cosmic Web
The critical acceleration scale derived from first principles:
QIC-S_Ver9.2/
├── Sasada_QIC-S_Ver9.2.pdf # Full paper (English)
├── phase_analysis.py # Phase Metric (M) calculation
├── qics_analyzer.py # Figure 1: Hamiltonian Landscape
├── plot_histogram.py # Figure 2: Phase distribution
├── plot_scaling_law.py # Figure 3: Universal scaling law
├── bootstrap_analysis.py # Figure 4: Bootstrap validation
├── requirements.txt # Python dependencies
├── results/
│ └── QIC_S_Result_N170.csv # Analyzed dataset
├── figures/
│ ├── Figure_1_NGC0100.png # Hamiltonian Landscape
│ ├── Figure_2_Phase_Distribution.png # Phase histogram (N=170)
│ ├── Figure_3_Universal_Scaling_Law.png # Universal scaling law
│ └── Figure_4_Bootstrap_Analysis.png # Bootstrap validation
├── LICENSE
└── README.md
- Python 3.8+
- NumPy, Matplotlib, SciPy, Pandas
# Clone the repository
git clone https://github.com/QuantumInfoCosmo/QIC-S_Ver9.2.git
cd QIC-S_Ver9.2
# Install dependencies
pip install -r requirements.txt# Figure 1: Hamiltonian Landscape visualization
python qics_analyzer.py
# Figure 2: Phase distribution histogram (N=170)
python plot_histogram.py
# Figure 3: Universal scaling law (galaxies + filaments)
python plot_scaling_law.py
# Figure 4: Bootstrap statistical validation
python bootstrap_analysis.pyNote: All scripts read data from results/QIC_S_Result_N170.csv.
The file results/QIC_S_Result_N170.csv contains pre-computed Phase Metrics and transport coefficients for all 170 SPARC galaxies meeting quality criteria.
| Column | Description |
|---|---|
Galaxy |
Galaxy identifier (SPARC ID) |
M |
Phase Metric (log-variance of Hamiltonian gradient) |
R |
Characteristic scale [kpc] |
D_eff |
Effective transport coefficient [kpc·km/s] |
Note: The classification (Order/Chaos) is determined by the threshold M = 0.5.
Rotation curve data derived from the SPARC database:
Lelli, F., McGaugh, S. S., & Schombert, J. M. 2016, AJ, 152, 157
http://astroweb.case.edu/SPARC/
The Phase Metric M quantifies dynamical state using log-variance of the Hamiltonian gradient:
where
Physical interpretation: Log-transformation extracts pure "entropic fluctuations" independent of scale, distinguishing laminar (Order) from turbulent (Chaos) information flow.
Represents scale-dependent effective dynamical coupling from a renormalization group perspective.
Important: The Phase Metric calculation methodology differs between versions.
| Version | Data Range | Example (NGC 6503) | Description |
|---|---|---|---|
| Ver 9.1 | Flat region only | M ≈ 0.17 | Calculated M using only the flat (outer) region of rotation curves |
| Ver 9.2 (Current) | All data points | M ≈ 0.57 | Updated to use complete rotation curve data for rigorous validation |
Key implications:
- Some galaxies (e.g., NGC 6503) show higher M values in Ver 9.2 due to inclusion of inner rotation curve regions with steeper velocity gradients
- NGC 6503 is reclassified from Order Phase (Ver 9.1) to Chaos Phase (Ver 9.2)
- The code in this repository reflects the Ver 9.2 methodology
This methodological refinement enhances robustness by capturing the full dynamical information content of each galaxy's rotation curve.
If you use this code or data, please cite:
@article{sasada2026qics,
author = {Sasada, Yoshiaki},
title = {Two-Tier Steady-State Cosmology and the Discovery of a Universal Scaling Law: {QIC-S} Theory Ver 9.2},
year = {2026},
month = {February},
doi = {10.17605/OSF.IO/9A3CD},
url = {https://doi.org/10.17605/OSF.IO/9A3CD}
}- SPARC Database: Lelli, McGaugh, & Schombert (2016), AJ, 152, 157
- Filament Rotation: Tudorache et al. (2025), MNRAS, 544, 4306
- ER=EPR Conjecture: Maldacena & Susskind (2013), Fortsch. Phys., 61, 781
- Conformal Interfaces: Komatsu, Kusuki, Meineri, & Ooguri (2025), arXiv:2512.11045
This research was assisted by AI systems (Claude for theoretical articulation and Gemini for numerical analysis). All physical interpretations and theoretical frameworks are the sole responsibility of the author.
This project is licensed under the MIT License - see the LICENSE file for details.
For questions regarding this research, please open an issue or contact via the repository.
Repository: https://github.com/QuantumInfoCosmo/QIC-S_Ver9.2