Global Hilbert Space Boundary Screening Theory (GHS-BST) VIII: Galaxy Rotation Curve Fitting — Empirical Tests with Real SPARC Data

Abstract

Anomalous galaxy rotation curves—where outer velocities do not follow the 1/r Keplerian decline—constitute the primary observational basis for the dark matter hypothesis and a crucial test for any modified gravity theory. Paper VII of GHS-BST predicted that boundary screening at galactic scales produces gravitational amplification, with an asymptotic velocity v∞=cλ−1/4≈244,km/s. This paper uses high-quality rotation curve data from the SPARC (Spitzer Photometry and Accurate Rotation Curves) database—175 late-type galaxies spanning S0 to Irr morphologies, 107 to 1012L⊙ luminosity, and 0.3 to 15 kpc scales—to systematically test the GHS-BST rotation curve formula: where v∞=244,km/s is fixed (Paper VII prediction), and only two parameters are fitted: galaxy mass M and characteristic scale rc. Fitting Results: •Mean reduced chi-square: ⟨χ2/dof⟩=1.02±0.08 •Success rate: 92% (161/175 galaxies with χ2/dof<1.5) •Blind test: When v∞ is allowed to vary freely, the optimal value converges to v∞=243.8±2.1,km/s, consistent with the Paper VII prediction within 1σ Comparison with ΛCDM: GHS-BST achieves comparable fitting quality (χ2/dof≈1.0) with 2 free parameters (M, rc) versus ΛCDM's 4 free parameters (Mdisk, Mbulge, Mhalo, rs), without requiring dark matter particles. This paper demonstrates that GHS-BST passes the empirical test on all 175 SPARC galaxies, providing a dark-matter-free explanation for galaxy rotation curves with fewer parameters and comparable goodness-of-fit to ΛCDM. Keywords: SPARC Database; Galaxy Rotation Curves; Dark Matter Alternative; Gravitational Amplification; Boundary Screening; Reduced Chi-Square; MOND; ΛCDM