Complete Joint Constraint-Kernel Realization Closure for the Wheeler–DeWitt System

Description Complete Joint Constraint-Kernel Realization Closure for the Wheeler–DeWitt System is the ninth paper in the Wheeler–DeWitt ARC. It brings the preceding canonical, quantum, temporal, covariant–canonical, and controlled semiclassical results into one jointly realized Wheeler–DeWitt constraint kernel. Its central question is: Given the surviving Wheeler–DeWitt realization, its admissible profile-clock structure, and its controlled covariant–canonical and semiclassical recoveries, what joint constraint kernel must be realized for the system to count as a complete physical realization rather than a collection of separately compatible constructions? The manuscript closes the relevant constraint roles together: the descended canonical gravity structure, refoliation conditions, integrated gravity–matter occupancy, differentiated quantum candidate data, renormalized quantum survival, and the qualified relational and semiclassical structures inherited from WDW‑7 and WDW‑8. The endpoint is not a formal conjunction of independently asserted conditions, but a jointly constrained realization in which the required roles coexist without loss of provenance, standing, or constraint compatibility. Its central passage is: [ \text{controlled Wheeler--DeWitt realization} \longrightarrow \text{joint constraint-kernel closure} \longrightarrow \text{complete physical realization of the Wheeler--DeWitt system}. ] The paper distinguishes the standing-bearing joint kernel from presentation-dependent representatives: a chosen foliation, clock profile, canonical chart, covariant presentation, semiclassical branch, or local solution form may support an admissible presentation, but cannot replace the jointly realized constraint system itself. WDW‑9 therefore does not treat a formal state satisfying one operator equation as sufficient for physical realization. Complete closure requires compatibility across the inherited gravitational, matter, redescription, refoliation, quantum-survival, and relational roles. The result supplies the completed joint-kernel input for the final global stage. WDW‑9 does not yet establish the global clock-neutral relational descent or universality closure of WDW‑10. Its load-bearing contribution is prior and narrower: it completes the joint realization closure of the Wheeler–DeWitt system on which that global result depends.