Covariant Multi-Scale Negative Coupling on Dynamic Riemannian Manifolds: A Geometric Framework for Topological Persistence in Infinite-Dimensional Systems
This paper introduces a geometric framework of Covariant Multi-Scale Negative Coupling on dynamic Riemannian manifolds to counteract dimensional reduction in dissipative PDEs, theoretically proving the finite dimensionality of global attractors while numerically validating the mechanism's ability to stabilize high-dimensional structural complexity against macroscopic dissipation.