No Dark Matter Required: Effective Gravitational Dimension D(R) Transitions to 2 in 116 of 171 SPARC Disk Galaxies

We analyze rotation curves of 171 disk galaxies from the SPARC database using a model-independent measure of effective gravitational dimensionality: D(R) = 2(1 - alpha), where alpha = d(log V)/d(log R). This quantity equals 3 for Keplerian (spherical) dynamics and 2 for flat rotation curves (disk geometry). We find that 116 of 171 galaxies (68%) have D within [1.5, 2.5] at their outermost radii, with a median of 1.87. The transition from D ~ 3 at inner radii to D ~ 2 at outer radii is a generic feature of disk galaxies. Galaxies that deviate are predominantly small dwarfs (R_max < 5 kpc) where the dimensional transition is incomplete. We show that the baryonic Tully-Fisher exponent of 4 follows analytically from the D: 3 to 2 transition, and that the MOND acceleration scale a_0 = cH_0/(2 pi) emerges as the transition boundary. These results suggest that dark matter halos may be unnecessary: the apparent mass discrepancy in disk galaxies is a consequence of applying three-dimensional gravitational formulae to effectively two-dimensional systems.