The Hydrodynamic Formalism of TES - Reproducibility Code

# TES Hydrodynamic Formalism: Reproducibility Package (v3.0)

This repository contains the official Python pipeline required to independently reproduce all findings, rotation curves, Machine Learning evaluations, and high-significance diagnostic metrics presented in the paper:

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

## Version 3.0: Major Diagnostic Update
This version (v3.0) extends beyond basic model validation, incorporating advanced statistical tests that establish the hydrodynamic nature of galactic kinematics:

* **2D Phase-Space Mapping:** Implementation of radial and gas-fraction phase-space diagnostics, revealing the structured 2D geometry of vacuum memory proxies.
* **$27\sigma$ Significance Residual Analysis:** Official scripts for the "Kinematic Deficit Paradox" test, quantifying the systematic correlation between vacuum memory and baryonic gas fraction ($p < 10^{-26}$).
* **Attractor-Collapse Evaluation:** Quantitative proof that the observed RAR scatter is a dynamical hysteresis (memory effect) rather than a stochastic error or a simple 1D modification of gravity.
* **Rigorous Cross-Validation:** Full integration of Leave-One-Out Cross-Validation (LOOCV) ensuring 86.15% out-of-sample predictive accuracy.

## Pipeline Overview: `TES_Hydrodynamic_Formalism_v3.ipynb`
The master notebook is organized into three primary analytical modules:

### 1. Machine Learning Validation Surrogate (LOOCV)
Performs "blind" prediction of the required vacuum memory ($S$) using only baryonic morphological features. This module establishes the $R^2 = 0.711$ predictive score, proving that the "missing mass" effect is deterministically encoded in the baryonic distribution.

### 2. Kinematic Engine & 2D Phase-Space Diagnostics
Models the Newtonian flow and applies the Viscous Lever-Arm mechanism. This module generates the 2D diagnostic maps that distinguish the TES framework from MOND and Dark Matter by revealing the gas-fraction and radial-rank dependencies of the kinematic residuals.

### 3. Information-Theoretic (BIC) & Residual Statistics
Executes a formal Bayesian Information Criterion (BIC) comparison ($\Delta\text{BIC} = +46.60$ against MOND) and performs the high-significance Spearman/Mann-Whitney tests on the RAR residuals.

## Data Requirements
The pipeline is designed for "One-Click Reproducibility". It **automatically fetches the SPARC database** (Lelli et al., 2016) directly from official repositories. No manual data management is required.

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

## Usage
Open `TES_Hydrodynamic_Formalism_v3.ipynb` in a Jupyter environment or Google Colab and select **"Run All"**. The notebook will generate all figures, accuracy scores, and the $27\sigma$ statistical distributions presented in the study.

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**DOI:** 10.5281/zenodo.19023050  
**License:** Open Source for Scientific Reproducibility