Geometrical Skewness in Einsteinian Kinetic Manifolds: A Deterministic 1D Framework for Galactic Dynamics and Emergent Torque

This work introduces a deterministic geometric framework for galactic dynamics within the Universal Meigooni Framework (UMF), serving as a foundational reference for subsequent atomic- and plasma-scale extensions. We present a deterministic geometric approach to galactic dynamics based on the Universal Meigooni Framework (UMF), introducing a third-order Skewness Tensor $\mathcal{S}_{ijk}$ as a geometric generalization of Einsteinian kinetic diffusion. By collapsing $N$-dimensional chaotic phase space into a stabilized one-dimensional complex manifold anchored at an invariant point, the framework enables deterministic computation of angular momentum redistribution and emergent torque. We define Manifold Torque $\tau_m$ as a geometric effect governed by a universal constant $\nu_V$, representing the equilibrium angular root of manifold skewness. The formalism reproduces flat rotation curves in spiral galaxies, velocity dispersion profiles in elliptical systems, environmental sensitivity in dwarf and irregular galaxies, and collective effects in interacting and cluster environments—without requiring additional non-baryonic matter components at the galactic scale. A first-principles derivation of the baryonic Tully–Fisher relation emerges naturally as a geometric consequence of stabilized kinetic dynamics.