Covariant–Canonical Reconciliation and Controlled Semiclassical Recovery for the Wheeler–DeWitt Constraint

Description Covariant–Canonical Reconciliation and Controlled Semiclassical Recovery for the Wheeler–DeWitt Constraint is the eighth paper in the Wheeler–DeWitt ARC. It reconciles the surviving canonical Wheeler–DeWitt realization with its covariant gravitational interpretation and determines the controlled semiclassical recoveries that remain faithful to the joint constraint system. Its central question is: Given the renormalized Wheeler–DeWitt realization and its admissible constraint-induced Cauchy-germ evolution, under what conditions can canonical and covariant presentations be reconciled, and what semiclassical structures may be recovered without replacing the constrained realization by an independently assumed background-time theory? The manuscript carries forward the connection-typed canonical provenance, groupoid-faithful descent, constrained refoliation, joint gravity–matter closure, configuration-space candidate construction, quantum constraint survival, and profile-clock analysis of WDW-1 through WDW-7. It tests the relation between canonical representatives and covariant gravitational structure while maintaining the distinction between standing-bearing constrained content and presentation-dependent choices. Its central passage is: [ \text{constraint-induced Cauchy-germ evolution} \longrightarrow \text{covariant--canonical reconciliation} \longrightarrow \text{controlled semiclassical recovery}. ] The recovered semiclassical structure is controlled rather than primitive. A background, clock, foliation, branch, or approximate Schrödinger-like presentation is admissible only where it is derived from and remains compatible with the realized Wheeler–DeWitt constraint. It cannot silently displace the joint constraint kernel, select a preferred fundamental time, or confer independent physical authority on one canonical or covariant representative. WDW-8 therefore does not identify the Wheeler–DeWitt constraint with an ordinary externally timed Schrödinger equation, nor does it claim unrestricted validity for every semiclassical approximation, deparametrization, or background-dependent quantization. Its result is a qualified recovery architecture: a clear account of which covariant–canonical correspondences and semiclassical presentations preserve the prior constrained realization. The paper supplies the reconciled and controlled input for the final ARC stages. WDW-9 addresses complete joint constraint-kernel realization closure; WDW-10 establishes global clock-neutral relational descent and universality closure.