Kernel-Native Upstream Continuation and Projection Intertwining under AASC

This paper constructs the common continuation-bearing history required by the physical unification of Einstein and Schrödinger dynamics. Building on the previously established operational source and common Casimir mass, it forms one upstream history within the Admissibility and Standing Constraint framework and proves that its gravitational and quantum projections reproduce the required Einstein and Schrödinger continuations. The projection maps preserve the same source, mass reference, identity, and overlap structure, preventing the two histories from becoming independently calibrated constructions joined only after the fact. By enforcing quotient stability and excluding projection backflow, endpoint-only matching, and representative multiplication, the paper converts structural common origin into an explicit dynamical realization and supplies the continuation carrier required for exact certificate-fibre exhaustion. 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.