Non-Euclidean Geometric Vortices as Gauge Fields for Mirror Matter Inter-Universal Coupling: A Gravitational AI Modeling Approach

The nature of the dark sector remains the deepest unresolved problem in observational cosmology. This preprint develops a theoretical and computational proposal in which the dark-matter phenomenology is produced by a mirror sector, a second copy of the Standard Model related to ours by a discrete exchange symmetry Z2, which interacts with our sector gravitationally and through a geometric gauge field. The gauge field topological excitations are non-Euclidean geometric vortices. To determine the vortex geometry from data we define a Gravitational Neural Network (GNN), a covariant message-passing network on a simplicial discretization of space, and we prove a convergence theorem for its fixed-point iteration under an explicit Lipschitz bound. We specify a spectral protocol based on FFT boundary regularization and unfolded level-spacing statistics compared with the Gaussian Unitary Ensemble (GUE) Wigner surmise.