GDG-QG-Certificate-IV: Global Consistency and Gravitational Admissibility

This record presents the fourth certificate in the Gamma-DG quantum-gravity program. Certificate-I established the existence of a bridge from the primitive Gamma-DG structure toward a spacetime-readable sector. Certificate-II introduced controlled readability through weak monotonicity, weak weighting, and barrier-sensitive organization. Certificate-III clarified how readability, causal structure, and emergent geometry can arise in a controlled regime. Certificate-IV addresses the next structural question: under what conditions can such a readable causal-geometric regime be regarded as globally consistent and gravitationally admissible? Rather than assuming a pre-given gravitational spacetime, this work identifies internal structural conditions under which an emergent readable geometry may be sustained as a coherent gravitational sector. It introduces the notion of gravitational admissibility, analyzes its associated global consistency requirements and obstruction patterns, and formulates Transfer Principle IV, which promotes controlled readable causal geometry to a gravitationally admissible regime under suitable hypotheses. The main result establishes a fourth certificate-level transition in the Gamma-DG program: from emergent geometry to a globally coherent gravitationally admissible sector.