An Exploratory Phenomenological Study of a Local Variable-Scale Propagator for Galactic Rotation Curves

**Abstract & Overview:**This record contains the complete research artifacts for an exploratory phenomenological study investigating a non-local velocity modification model based on a variable-scale propagator applied to galactic rotation curves[cite: 4]. **Key Highlights of the Study:*** **Empirical Analysis:** Evaluated across all 175 disk galaxies in the SPARC (Spitzer Photometry and Accurate Rotation Curves) database without individual galaxian parameter tuning[cite: 4, 5].* **Performance Metrics:** Achieves an unweighted global root-mean-square error (RMSE) of $38.78 \text{ km/s}$ across 3,345 data points[cite: 4, 5].* **Scale Invariance & Compact Objects:** Examines the dimensionless relaxation scale parameter $\eta = l_0 / (GM)$, bridging galactic scales with compact objects such as the supermassive black hole $M87^*$ ($\eta \approx 1.289$)[cite: 4, 5, 6].* **Asymptotic Limits & Transparency:** Rigorously analyzes the asymptotic regime ($r \to \infty$), uncovering a fundamental mathematical limitation where the predicted logarithmic slope $d\ln V_{\text{flat}}/d\ln M = (1+\eta)/2$ approaches $0.50$ ($\eta \ll 1$), thereby diverging from the empirical requirements of the Baryonic Tully-Fisher Relation (BTFR slope $\approx 0.25$)[cite: 4, 6]. **Included Files in this Dataset:**1. `Baryonic Valve Exploratory Paper.pdf` — The full 3-page exploratory research paper[cite: 4].2. `baryonic_valve_sparc_analysis.ipynb` — The fully reproducible Jupyter Notebook containing data parsing, model execution, and asymptotic plotting pipelines.3. `baryonic_valve_sparc_analysis.py` — Standalone Python script for local execution.4. `baryonic_valve_sparc_analysis_results.csv` — Detailed galaxy-by-galaxy numerical output metrics for the 175 SPARC profiles. **Author:** Mounir Djebassi (INAS - International Network of Algerian Scientists)[cite: 4]. **ORCID:** [0009-0009-6871-7693](https://orcid.org/0009-0009-6871-7693)[cite: 4] **GitHub Repository:** [djebassimounir-dev](https://github.com/djebassimounir-dev)[cite: 4]