The Maelstrom Theorem: Global Boundedness and Attractor Homology via Contorsion Dynamics on (2n + 1)-Dimensional Regular Contact Manifolds

This paper establishes a rigorous geometric framework for non-conservative, dissipativedynamical systems on smooth, connected (2n + 1)-dimensional regular contact manifolds.By relaxing the pseudo-Riemannian assumption of symmetric connections, we evaluate theintrinsic interaction between non-linear vector fields and non-vanishing contorsion tensorsunder Cartan structure equations. We introduce the Maelstrom Theorem, proving thatan explicit geometric stiffness condition—derived from the contraction of the contorsiontensor field—forces the trajectory flow to be globally bounded and strictly non-divergentwithout the imposition of ad-hoc damping parameters. By utilizing generalized Clarkesubdifferentials, we formally resolve the non-differentiability challenges typically encounteredat the geodetic cut locus, showing that the flow is globally transverse to these singularitystrata. Furthermore, we demonstrate that the compact boundary subvariety constitutesan asymptotically stable global attractor whose Reeb flow homology yields a rigid, strictlypositive topological invariant. Finally, we project this mechanism onto a five-dimensionalcontact space to show how low-dimensional restrictions naturally recover discrete actions astopological invariants.