Rotational Organization Theory of Gravitational Concentration: A Fiber-Bundle and Persistent-Homology Framework for Hierarchical Structure Formation

This work presents the Rotational Organization Theory of Gravitational Concentration (ROTGC), a theoretical framework that investigates the dynamical organization of self-gravitating systems while remaining fully consistent with Newtonian gravity and General Relativity. Rather than modifying gravity, the theory studies how angular-momentum transport, rotational organization, shear, torque, and matter-energy transport contribute to the historical formation of gravitationally concentrated structures. The framework introduces a conservation-based formulation, differential geometric representation through fiber bundles and Ehresmann connections, and optional topological characterization using persistent homology to describe hierarchical structure formation across astrophysical scales. The manuscript provides explicit falsification criteria and identifies observational tests involving galaxy rotation curves, weak gravitational lensing, compact objects, gravitational waves, and large-scale structure.