The 3.998D Manifold Framework: Assessment of Geometric Unification and the Resolution of Galactic Rotation Anomalies

This paper presents the results of the application of the 3.998D Manifold Framework, a geometric theory that posits all physical phenomena emerge from a scalar field (ϕ-Field) within a space of spectral dimension d_s=3.998 and a dimensional deficit of δ=0.002. Unlike standard cosmological models that require Dark Matter and Dark Energy to resolve dynamic anomalies, this framework introduces a single density-dependent mechanism governed by a manifold stiffness constant (β_eff ≈ 5.01). The proposed Framework further demonstrate that this constant is the geometric reciprocal of a 13.4% metric compaction, providing a structural bridge that unifies subatomic bond tension with galactic dynamics. Analysis shows that this geometric constraint successfully unifies physics across subatomic, galactic, and cosmic scales. Statistical modelling of galactic rotation curves for the Milky Way, Andromeda (M31), Triangulum (M33), UGC 128, and NGC 2403, demonstrates that the framework’s saturation mechanism replaces the need for invisible mass, achieving statistically significant improvements over Newtonian predictions while recovering standard gravity in high-density solar systems.