The Hydrodynamic Formalism of TES - Reproducibility Code

# TES Hydrodynamic Formalism: Reproducibility Package (v2.0)

This repository contains the official Python pipeline required to independently reproduce all findings, rotation curves, Machine Learning evaluations, and Bayesian Information Criterion (BIC) metrics presented in the paper:

**"The Hydrodynamic Formalism of TES: Modeling Galactic Rotation Curves via Viscous Lever-Arm Vacuum Memory"** by George Kozas.

## Version 2.0 Updates
This updated package (v2.0) reflects the finalized methodological refinements of the manuscript:
* **Consolidated Pipeline:** All individual scripts have been integrated into a single, high-performance Jupyter Notebook for easier execution and visualization.
* **Rigorous Validation:** Implementation of strict Leave-One-Out Cross-Validation (LOOCV) and physical feature selection.
* **Refined Statistics:** Updated metrics including the $R^2 = 0.711$ predictive score and the $\Delta\text{BIC} = +46.60$ information-theoretic advantage.

## Pipeline Overview: `TES_Master_Pipeline_v2.ipynb`

The master notebook is organized into three primary analytical modules:

### 1. Machine Learning Validation Surrogate
Performs the LOOCV using a Random Forest algorithm. It maps four canonical, non-circular baryonic features (gas fraction, disk concentration, kinematic deficit, and laminar slope) to the analytically required vacuum memory ($S_{ideal}$). This demonstrates that the "missing mass" effect is deterministically encoded in the baryonic distribution.

### 2. Kinematic Modeling & Renzo's Rule
Extracts kinematic data from the SPARC database, models the Newtonian flow, and applies the Viscous Lever-Arm Coupling. It reproduces the analytical rotation curves and executes the statistical tests (Spearman $\rho \approx 0.657$) demonstrating that vacuum memory is dynamically driven by the collisional gas phase.

### 3. Information-Theoretic Comparison (BIC)
Executes a formal Bayesian Information Criterion (BIC) comparison. It evaluates the TES model (zero per-galaxy parameters) against MOND ($k=1$) and Pseudo-Isothermal Dark Matter Halos ($k=2$), quantifying the complexity-penalty advantage of the TES framework.

## Data Requirements
The pipeline is configured to **automatically fetch the SPARC database** (Lelli et al., 2016) directly from official repositories via automated web requests. No manual data downloading or local CSV management is required to initiate the analysis.

## Dependencies
To execute the pipeline, the following Python libraries are required:
* `numpy`
* `pandas`
* `matplotlib`
* `scipy`
* `scikit-learn`

## Usage
Simply open `TES_Master_Pipeline_v2.ipynb` in a Jupyter environment (or Google Colab) and "Run All". The notebook will generate all figures, accuracy scores, and statistical distributions presented in the study.