Common Mass-Charge Matching and Universal Inertial–Active Proportionality under AASC

This paper derives gravitational and inertial mass from one conserved source-generated charge within the Admissibility and Standing Constraint framework. Beginning with the operational stress–energy source constructed in the preceding module, it forms the translation charge and identifies the corresponding Poincaré Casimir as the common mass coordinate carried by both the gravitational and quantum descriptions. The analysis shows that gravitational monopole mass and inertial Hamiltonian mass are not independently calibrated quantities later set equal, but lawful projections of the same standing-bearing invariant. By preserving source identity, sector conditions, normalization, and quotient stability, the paper supplies the shared mass reference required for a common Einstein–Schrödinger continuation and the completed gravity–quantum realization certificate. 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.