Information Dynamics Inversion for Planet Nine

This repository contains a Python implementation to invert the Information Dynamics parameters for the hypothetical Planet Nine using the argument of perihelion (ω) distribution of extreme trans-Neptunian objects (ETNOs). The code downloads the latest MPCORB database, selects ETNOs, performs a fixed‑window clustering test, and fits a mixture of two von Mises distributions to extract the concentration parameter κ, information purity p_ID = κ/(1+κ), and the self‑organization to dissipation ratio ε/γ = p_ID/(1−p_ID).

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1. Purpose

The aim is to provide a quantitative, data‑driven estimate of the dynamical state of the outer Solar System within the Information Dynamics framework. Instead of assuming a conventional massive planet, the observed N=2 symmetry in ETNO orbits is interpreted as a projection of an information field. The inverted parameters offer a direct, testable characterization of this field.

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2. Method

1. Data source The Minor Planet Center Orbit Table (MPCORB.DAT), contains orbital data of hundreds of thousands of small celestial bodies (including orbital elements, absolute brightness, latest observation data, etc.)

   1. I have uploaded MPCORB.DAT file accompanying the code.
   2. You may download MPCORB.DAT file manually from https://www.minorplanetcenter.net/data/.
   3. The script could automatically download the Minor Planet Center’s MPCORB.DAT file (gzipped) if not already present.

2. ETNO selection
   Objects are selected with:

   • semi‑major axis (a > 200) AU
   • perihelion distance (q = a(1-e) > 30) AU
   • absolute magnitude (H > 5)

3. Statistical clustering test
   A fixed window half‑width of 60° is used to measure the fraction of ETNOs whose ω falls within two opposite windows (centered on a test longitude ωₚ₉ and ωₚ₉+180°). The best‑fitting ωₚ₉ is found by scanning 0–360°. Significance is assessed with 10,000 Monte Carlo trials against a uniform distribution.

4. Information Dynamics parameter inversion
   The ω distribution is modelled as a mixture of two von Mises distributions with equal concentration κ and means separated by 180°. Maximum likelihood estimation yields κ.

   The information purity is defined as:

   p_ID = κ / (1 + κ)

   and the self‑organization to dissipation ratio as:

   ε / γ = p_ID / (1 - p_ID)

   Bootstrap resampling (1000 trials) gives 68% confidence intervals.

5. Visualization

   • A polar rose plot of the ω distribution (planet_nine_rose.png).
   • A histogram with the fitted von Mises mixture density (planet_nine_von_mises_fit.png).

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3. Requirements

• Python 3.6+
• Required packages: numpy, pandas, matplotlib, scipy, requests

Install them with:

pip install numpy pandas matplotlib scipy requests

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4. Usage

Clone the repository and run the script:

git clone https://github.com/hkaiopen/InformationDynamics_PlanetNine.git
cd InformationDynamics_PlanetNine
python planet_nine_inversion.py

The script will:

• Download MPCORB.DAT if missing (about 30–40 MB, takes a few seconds).
• Process the data and output results to the console.
• Save the two plots in the current directory.

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5. Output example

ETNO found: 43 (a > 200 AU, q > 30 AU, H > 5)

=== Fixed-window test (half-width=60°) ===
Best ω_P9 = 356.0°
Clustering fraction = 83.7% (36/43)
Monte Carlo p-value: 0.0107

=== Information Dynamics Parameter Inversion ===
Best ω_P9 = 8.2° (68% CI: [0.0, 21.8])
Concentration κ = 1.22 (68% CI: [0.80, 1.86])
Information purity p_ID = 0.550 (68% CI: [0.444, 0.651])
Self-organization/dissipation ε/γ = 1.223

The best ωₚ₉ from the von Mises fit (8.2°) is equivalent to 356° (the fixed‑window result) because the mixture is symmetric under adding 180°.

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6. Interpretation

• κ = 1.22: Moderate concentration – the ETNO ω distribution is clearly non‑uniform but not extremely peaked.
• p_ID = 0.55: The system is moderately self‑organized (ε slightly larger than γ). This places the outer Solar System between the highly ordered interstellar object 1I/‘Oumuamua (p≈0.83) and the thermally dominated comet 2I/Borisov (p≈0.09).
• ε/γ = 1.22: Self‑organization is only about 22% stronger than dissipation, implying a “gentle shepherd” rather than a rigid structure.

These parameters provide a quantitative description of the hypothetical Planet Nine as an information field eigenmode, and they make specific, testable predictions for future surveys (e.g., LSST).

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7. Repository contents

• planet_nine_inversion.py – Main Python script (as described above)
• README.md – This file
• (Plots are generated on the fly and not stored in the repository)

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8. License

This project is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0).

This license allows you to:

• Share — copy and redistribute the material in any medium or format.
• Adapt — remix, transform, and build upon the material.

Under the following terms:

1. Attribution (BY) — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use1.
2. NonCommercial (NC) — You may not use the material for commercial purposes. Commercial purposes include, but are not limited to:
   • Selling products or services that incorporate this project.
   • Using it in paid training or courses.
   • Integrating it into commercial software.
   • Any use aimed at monetary compensation or private financial gain.
3. ShareAlike (SA) — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original (CC BY-NC-SA 4.0)1.

For any commercial use, you must obtain prior written permission from the author. Please contact the author to discuss licensing options.

To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/4.0/.

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Support This Independent Research

If you feel excited on this unifying framework and would like to support further development (simulations, data analysis, outreach), any contribution — big or small — is deeply appreciated. We definitely call for Research Funding and Collaboration and are deeply committed to the highest standards of Scientific Responsibility.

Donation Options

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• Bank transfer Please DM me on X (@KevinHuangkai) for bank details.

All funds go toward researching more mysteries in the universe, and expanding the Information Dynamics model.
Thank you for supporting open, frontier science!

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9. Citation

If you use this code or the results in your own work, please cite the following works:

1. The associated research paper (preprint):

   Huang, K., & Liu, H. (2026). Information Dynamics: Gravity as a Projection of the Information Field – Inversion and Test via the Orbital Clustering of Planet Nine. Zenodo preprint. (Updated on Mar 31, 2026 https://doi.org/10.5281/zenodo.19319558 This DOI represents all versions, and will always resolve to the latest version).

2. The software implementation (this repository):

   Huang, K. (2026). hkaiopen/InformationDynamics_PlanetNine: v1.0 (Version v1.0) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.19208434

In the acknowledgements section of any publication, we also encourage you to acknowledge the use of data from the Minor Planet Center, as per their request:

This research has made use of data and/or services provided by the International Astronomical Union's Minor Planet Center.

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For any questions or suggestions, please open an issue or contact the authors.