Classical Matter Occupancy and Joint-Constraint Closure under AASC

Description Classical Matter Occupancy and Joint-Constraint Closure under AASC is the fourth paper in the Wheeler–DeWitt ARC. It extends the refoliation-faithful canonical gravity realization established in WDW-1 through WDW-3 to include classical matter as an integrated, jointly constrained occupant. Its central question is: Given a globally descended and refoliation-faithful canonical gravity realization, under what conditions can classical matter be incorporated without becoming an external attachment or disrupting the joint gravitational constraint system? The manuscript carries matter configuration and momentum roles, source-bearing content, and their Hamiltonian and momentum-constraint contributions into the inherited canonical realization. The result is a joint gravity–matter constrained structure, rather than a gravity-only canonical skeleton to which matter is later appended informally. Its central passage is: refoliation-faithful canonical gravity realization⟶classical matter occupancy⟶joint gravitational–matter constraint closure. Matter occupancy must preserve the connection-typed inheritance of WDW-1, the proper-redescription descent and boundary-standing protections of WDW-2, and the constrained-refoliation conditions of WDW-3. Field coordinates, foliation labels, canonical representatives, and chart-dependent expressions remain presentational structure; they cannot independently alter the standing-bearing Einstein–source realization or its constraint roles. WDW-4 thus supplies the completed classical gravity–matter input for the quantum stages of the ARC. It ensures that later configuration-space differentiation and Wheeler–DeWitt candidate construction act on a jointly closed constrained system, rather than quantizing an isolated gravitational sector. The paper does not yet construct the Wheeler–DeWitt candidate family, establish quantum constraint survival, or prove renormalized physical realization. Its load-bearing role is the integration and closure of classical matter within the inherited canonical and refoliation-faithful realization.