Gravitational Vortex Theory (LVG): The Chourahbil Constant κC = 0.01 kpc⁻¹ — Validation on 175 SPARC Galaxies

We present the Gravitational Vortex Theory (LVG), a modified gravity framework in which the rotation of baryonic matter excites a scalar field ψ(r), solution of a modified Helmholtz equation, producing an additional centripetal acceleration without invoking dark matter. The theory introduces a single universal constant, the Chourahbil Constant κC = 0.01 kpc⁻¹. With two free parameters per galaxy (V∞ and rc), LVG achieves χ² = 0.654 on 20 galaxies (Begeman 1989; Walter et al. 2008) and χ² = 2.273 on the complete 175-galaxy SPARC sample (Lelli et al. 2016), with a median of 0.524 and 134/175 excellent fits (77%). Results are reproduced across two independent runs (Δχ² < 0.03). The MOND reference on the same sample yields χ² ~ 1.5–2.5 (Li et al. 2018); LVG falls within this range. A fundamental identity V∞ ≡ Vflat is confirmed to 0.07% on 175 galaxies. The manuscript and code are distributed under the Creative Commons Attribution Non Commercial No Derivatives 4.0 International licence (CC BY-NC-ND 4.0). Rotation curve data are from the SPARC database (Lelli et al. 2016), available under CC-BY at http://astroweb.cwru.edu/SPARC/