The Big Bang as Boundary–Driven Initialization: A Sourced FRW Completion in the ψ₀–OCM

This work examines the Big Bang within the ψ₀–OCM (Osborne Cosmological Model), interpreting it as a boundary–driven initialization event rather than a physical singularity. The early universe is described as a routing–dominant redistribution regime that injects radiation into an emergent Friedmann–Robertson–Walker (FRW) domain prior to the formation of stable mass invariants. Standard General Relativity and gauge–invariant cosmological perturbation theory are preserved as effective descriptions valid after Redistribution–Locked Zone (RZL) stabilization. The paper introduces a covariant source term governing radiation injection derived from boundary flux conversion and constructs a fully gauge–invariant bridge to the curvature perturbation ζ. Explicit limits are shown in which the framework reduces exactly to modulated reheating and curvaton scenarios. Near scale invariance of the primordial spectrum arises from a simple class of ψ₀–time kernel scalings, providing the ψ₀–OCM analogue of quasi–de Sitter expansion. No modification of Einstein gravity or standard perturbation theory is required; the ψ₀–OCM supplies a physical closure for cosmological source terms that are otherwise treated phenomenologically.