The Phantom Metric: Parameter-Free Galactic Kinematics & Lensing

This repository contains the Python verification scripts and datasets used to test The Phantom Metric—a discrete geometric framework that models galactic anomalies (flat rotation curves and strong gravitational lensing) strictly via baryonic mass and spatial topology, eliminating the need for Dark Matter parameters.

📊 The Data & Results

The algorithms in this repository process raw observational data to predict kinematic and lensing behavior with zero free parameters and zero localized curve-fitting:

1. Gravitational Lensing (SLACS Audit):
   • Processes 100 strong elliptical lenses from the NASA/HST SLACS survey.
   • Result: Predicts the Einstein Ring Bounding Box ($R_{BB}$) strictly from visible mass with an accuracy of R² = 0.9917.
2. Galactic Kinematics (SPARC Audit):
   • Processes 3,391 spatiotemporal data points across 175 Late-Type Galaxies (LTGs).
   • Result: Achieves an unfiltered global goodness-of-fit of R² = 0.9150 using a strictly locked stellar mass-to-light ratio ($M/L = 0.46$).

🚀 How to Run the Code

Prerequisites

Make sure you have Python 3.8+ installed along with the required data science libraries:

pip install numpy pandas matplotlib scipy

Execution
Run the specific audit scripts directly from your terminal.

For the Lensing Audit (SLACS):
python SLACS_Phantom_Metric_Lensing.py
Outputs the statistical R² validation and generates figure3_lensing_audit.png.

For the Kinematics Audit (SPARC Global):
python SPARC_Global_Audit.py
Outputs the consolidated R² variance for all 175 galaxies and generates figure2_global_audit_ml046.png.

For the Single Galaxy Benchmark (NGC 2403):
python NGC2403_Benchmark.py
Outputs the single rotation curve fit and generates figure1_ngc2403_locked.png.

📄 Documentation
The full theoretical framework, mathematical derivations (including the formulation of the Topological Latency function and the Information-Theoretic Bounding Box), and the pre-print paper can be found at:

Zenodo Repository: https://doi.org/10.5281/zenodo.21920452

🤝 Open Science
True science is transparent. You are encouraged to download the datasets, run the Python scripts, manipulate the code, and verify the predictive power of this metric yourself.