Node 734: An Effective Weak-Field Geometric Model for Galactic Halo Dynamics

Node 734 presents an effective weak-field geometric model for galactic halo dynamics, applicable at halo scales (r ≳ 1 kpc). A logarithmic correction to the Newtonian gravitational potential is introduced, parameterized by a single coupling constant γ with dimensions of velocity squared. The model reproduces the flattening of galactic rotation curves in the weak-field regime without invoking non-baryonic dark matter. Dimensional consistency is verified explicitly. The regime of validity is defined: the model applies to large-scale galactic halos and does not extend to the strong-field domain near compact central objects such as Sagittarius A*. The present work is restricted to the effective weak-field formulation and does not address the underlying geometric origin of the correction term.