Dynamics of Galactic Systems in a Continuous Symmetry Substrate

Galactic systems are traditionally described within classical stellar dynamics and particle dark-matter models, in which collisionless matter evolves under Newtonian gravity or its relativistic extensions. In this work, we reinterpret these structures within a continuous symmetry substrate, where all matter and motion arise as localized topological deviation in a complex scalar field governed by global continuity constraints. Within this framework, conservation of phase-space density is not taken as axiomatic but emerges from the requirement that the substrate cannot tear and its phase topology must be preserved. We propose that unresolved fractional phase windings—unclosed topological defects of the phase field—contribute an effective gravitational density without forming particle-like excitations. A phenomenological model is developed showing that this fractional structure produces halo density profiles consistent with observed asymptotically flat galactic rotation curves. A central result is the reinterpretation of energy as a quantitative measure of symmetry deviation within the substrate. Physical structure, from particles to galaxies, is understood as stable configurations of this deviation, regulated by a universal complexity threshold separating a permissive regime of structure formation from an enforcing regime associated with black holes. In this view, black holes act not as singular endpoints but as regulatory transitions that redistribute excessive structural complexity. This framework provides a unified interpretation of galactic dynamics, gravitational lensing, cluster behaviour, and cosmic expansion without invoking particulate dark matter or a cosmological constant. It further suggests that compact, black-hole-dominated systems may arise from localized threshold crossings in the substrate, offering a natural interpretation of recently observed high-redshift compact sources. The resulting theory yields distinct, testable predictions and provides a coherent alternative perspective on gravitational structure and cosmology.