Galaxy Rotation Curves from the Baryonic Three-Population Model: A Quantitative Test Using 175 SPARC Galaxies

This paper tests the Progressive Matter-Antimatter Asymmetry (PMAA) framework's predicted 13:1 unstructured-to-structured baryonic matter ratio against 175 galaxy rotation curves from the SPARC database. Using a pressure-supported beta-model halo (β = 2/3), the analysis fits each galaxy with a single free parameter — the core radius r_c — while the halo mass is fixed by the framework's prediction.

Key results:

• Mass prediction confirmed: Optimal halo mass fraction f_halo = 1.088 ± 0.161 (bootstrap SE, 95% CI: [0.798, 1.350]), placing the predicted f_halo = 1.0 at 0.55σ. The local ratio R = 14.1:1 (95% CI: [10.4, 17.6]) contains the framework's full predicted range of 13:1 to 19:1.
• Profile physics confirmed: Optimal median χ²_red = 0.86 across 99 quality-1 galaxies when both mass and shape are fitted.
• Core-cusp problem resolved: The beta-model produces cored density profiles from gas physics alone, naturally matching the flat inner rotation curves that have contradicted NFW cusps for over 20 years.
• Parameter economy: PMAA uses 1 per-galaxy parameter (r_c) + 1 framework prediction (13:1). NFW uses 2 per-galaxy parameters (M₂₀₀, c) + 0 predictions, with its concentration-mass relation derived from ΛCDM simulations.
• Model-independent inputs: All inputs — measured rotation curves, photometry, gas maps, and established gas physics — are independent of cosmological model assumptions. No Big Bang cosmological parameters enter the computation.

The gravitational mass discrepancy traditionally attributed to dark matter is accounted for by unstructured baryonic matter, as independently confirmed by detections of the COS-Halos circumgalactic medium and Fast Radio Burst dispersion measures.

This is a companion paper to "Progressive Matter-Antimatter Asymmetry: A Quantitative Framework Derived from Genesis 1" (DOI: 10.5281/zenodo.18931071).