Rotational Organization Theory of Gravitational Concentration: A Fiber Bundle and Persistent Homology Approach to Hierarchical Structure Formation

Rotational Organization Theory of Gravitational Concentration (ROTGC) presents a conservation-based framework for studying the long-term organization of self-gravitating systems without modifying Newtonian gravity or General Relativity. The theory proposes that hierarchical rotational organization, differential rotation, shear, torque generation, and angular-momentum transport collectively govern the evolution of central matter-energy concentration across astrophysical systems. Version 2.0 develops the framework from established conservation laws before introducing advanced mathematical structures. Differential geometry, fiber bundles, persistent homology, sheaf-theoretic methods, and coordinate-independent formulations are employed as mathematical representations rather than additional physical assumptions. The theory introduces measurable definitions of central concentration, rotational organization, and net angular-momentum transport while preserving compatibility with General Relativity, continuum mechanics, and modern astrophysics. It provides explicit observational predictions using galaxy rotation curves, weak gravitational lensing, accretion disks, compact objects, black holes, Event Horizon Telescope observations, gravitational-wave catalogs, and large-scale structure surveys. ROTGC is proposed as a falsifiable theory of gravitational organization rather than a replacement theory of gravity. It introduces no new fundamental forces, matter components, or independent physical fields, and specifies clear observational failure criteria based on independent predictive performance and statistical validation.