Universal Branching as a Redistribution Outcome A ψ₀-OCM Interpretation of Flow Constrained Structure Formation

Branching structures recur across natural systems, including river networks, plant roots and vascular systems, neural arbors, electrical discharges, and the filamentary large-scale structure of the universe. While such patterns are commonly explained through domain-specific mechanisms, their repeated convergence toward similar topologies suggests the presence of a deeper unifying principle. This paper formulates branching as a generic outcome of constrained redistribution within the ψ₀-OCM (Osborne Cosmological Model). A minimal transport functional with a superlinear throughput penalty is introduced, and general convexity arguments show that hierarchical bifurcation reduces global transport cost once a finite branching overhead is exceeded. This yields a dimensionless branching criterion and a scaling proposition relating hierarchical depth to throughput. A central contribution of the paper is the explicit separation between topology selection and temporal evolution. Branching is shown to arise from atemporal constraint selection, while physical time governs only the rate at which systems converge toward a stable routing configuration. This distinction is formalized through the introduction of ψ₀-time as an ordering parameter for redistribution and stabilization, allowing branching onset to be expressed as a state-crossing condition rather than a time-triggered event.