Mechanical Origin of Orbital and Galactic Flatness: Manifold Efficiency and the Resolution of Dark Matter

The structural prevalence of disk-shaped systems is a fundamental characteristic of the observable universe, yet standard astrophysics relies on dissipative gas dynamics to explain this organization. This paper provides a deterministic mechanical derivation for orbital and galactic flatness using the Universal Sheet Tension (UST) Model. We propose that matter (3D inclusions) physically separates two primordial 2D manifold sheets, creating an anisotropic tension gradient. We demonstrate that the equatorial plane represents the state of minimum manifold stress (Potential Well), which effectively locks satellite bodies into 2D configurations. Furthermore, we derive the mathematical focusing of gravity within the disk plane, providing a purely geometric resolution to galactic rotation curves without the requirement for dark matter.