The Skateboard Theorem / Universal Global Stability of Baseline Flows via Asymmetric Affine Connections

We establish a foundational geometric constraint within the framework of dynamicalsystems on differentiable manifolds. We introduce and prove The SkateboardTheorem, an absolute structural restitution principle on smooth, metric-compatiblemanifolds featuring asymmetric affine connections. We demonstrate that for an autonomousdynamical system evolving on an N-dimensional Riemann-Cartan manifoldM, a volume-preserving non-linear perturbation field with compact support issubjected to an intrinsic geometric contraction driven by the properties of the backgroundconnection. Utilizing the direct method of Lyapunov stability combined withthe algebraic antisymmetry of the contorsion tensor and the Gauss divergence theorem,we prove that a volume-expanding baseline reference flow constitutes a GlobalAsymptotically Stable Attractor. This topological framework establishes a rigorousmathematical engine from which multi-scale cosmological damping mechanisms canbe derived as exact geometric corollaries.