Complete Certificate Closure for a Constraint-Native Gravity–Quantum Realization under AASC

This paper completes the physical realization of Einstein–Schrödinger structural unification. It integrates the independently established operational source, common Casimir mass, upstream continuation, gravitational and quantum projections, and exact certificate-fibre exhaustion into one dependency-controlled realization certificate. The manuscript verifies theorem-import fidelity, shared physical reference, projection intertwining, interface commutativity, record and boundary attachment, and complete evidence-graph closure. It proves that every mandatory target role is occupied and that, within the frozen target and declared comparison class, no second inequivalent lawful realization survives. The result is uniqueness modulo full certificate-preserving equivalence, not raw uniqueness of gauges, phases, charts, or other representatives. It provides the terminal constructive closure of the gravity–quantum unification ARC. Gravity as Structural Necessity — establishes the necessary physical constraint role; Einstein Dynamics — derives the unique minimal first-response metric projection; Schrödinger Dynamics — derives the corresponding minimal Hamiltonian quantum projection; Structural Unification — proves that the gravitational and quantum descriptions are projections of one admissible physical interior; Module A — completes operational metric–source attachment. Module B — proves common mass–charge matching. Module C — constructs common upstream continuation and projection intertwining. Module D — establishes exact certificate-fibre exhaustion and unique lawful role occupancy. Complete Certificate Closure — integrates the full FEP-1.0 gravity–quantum realization certificate.