Exact Certificate-Fibre Exhaustion and Unique Role-Occupancy Closure under AASC

This paper completes the exact target-fibre analysis required for the physical realization of Einstein–Schrödinger structural unification. It imports the independently constructed operational source, common Casimir mass, and upstream continuation, then assigns these and the associated projection, record, compatibility, boundary, and reference structures to the frozen FEP-1.0 target roles. The manuscript proves that every mandatory fibre is lawfully occupied, all shared interfaces close, and no inequivalent admissible assignment survives within the declared comparison class. Its uniqueness result is quotient-faithful: gauges, charts, phases, and other representative differences are removed only when they alter no standing-bearing certificate predicate, while differences affecting continuation, coverage, compatibility, boundary attachment, or endpoint standing remain visible. The result supplies the final standalone realization theorem required by the integrated certificate capstone. 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.