Environmental Transition Cosmology (ETC) - Chapter IV: Gravitational Phase Transition, Stochastic Gravitational Wave Background (SGWB), and Ultimate Model Testing

As Chapter IV of the Environmental Transition Cosmology (ETC) monograph, this paper formulates the early gravitational phase transition and the origin of the Stochastic Gravitational Wave Background (SGWB). In ETC, the transition from dense primordial nodes to the expanding universe occurs via environmental tunnels and hydrodynamic flux. Turbulent fluctuations across the tunnel cross-section and the phase-transition filter generate a characteristic SGWB in the nanohertz band, aligning with signals detected by Pulsar Timing Arrays (NANOGrav/EPTA) without invoking cosmic inflation or dark energy. Finally, explicit falsification criteria and ultimate observational tests are established