The Quasi-2D Origin of Flat Rotation Curves, the Tully-Fisher Relation, and the Cosmological Dimensionality Shift

We present a unified mathematical framework resolving the galactic kinematics anomaly without postulating Dark Matter. By synthesizing the fluid mechanics of primordial vorton collapse, the cosmological regime shift of the expanding metric, and the orthogonal projection mechanics of the Representation Boundary Principle, we prove that gravitationallybound systems preserve a quasi-2D+ topology inherited from the early universe. We rigorously formalize this as an exact topological projection Π2D+ from the continuous 3D unconstrained vacuum. This projection natively enforces a ∂2/zϕ = 0 spatial constraint, yielding the logarithmic potential derived by Sen (2020). We derive the flat galactic rotation curve and the Baryonic Tully-Fisher relation as exact geometric invariants of this manifold. Consequently, we prove that “Dark Matter” is not a physical particle, but the mathematical representation residue ∥(I − Π2D+)X3D∥2 erroneously discarded when astrophysics applies continuous 3D spherical accounting to a 2D+ projected topological space.