Unified Flow–Coherence Theory (UFCT): A Flow-Based Framework for Cosmic Structure, the Matter Cycle, and Gravitational Collapse

Abstract We present a mathematical framework for the Unified Flow–Coherence Theory (UFCT), based on a single postulate: the existence of a primordial cosmic vector flow field transporting total energy from regions of higher to lower concentration. From this postulate, the framework derives the continuity and flow-acceleration equations, the Scalar Coherence field (Q), the effective electromagnetic induction intensity (I_EM), the buoyancy stability criterion, the Schwarzschild horizon as a flow-speed limit, and a locally conserved energy density motivated by Noether symmetry. The coupling constants are constrained by classical limits, dimensional consistency, and observational correspondence, without introducing galaxy-dependent fitting parameters. Within this framework, coherent electromagnetic induction is proposed to regulate the formation, structural stability, and evolutionary cycle of matter within the cosmic flow, while black holes are interpreted as the upper saturation limit of this process. The theory provides a unified flow-based interpretation of structure formation, gravitational collapse, and the matter cycle, together with observational predictions that are, in principle, testable through galaxy dynamics, weak gravitational lensing, gravitational-wave ringdown, and black-hole imaging.