Groupoid-Faithful Proper-Redescription Descent of the AASC Canonical Gravity Realization

Description Groupoid-Faithful Proper-Redescription Descent of the AASC Canonical Gravity Realization is the second paper in the Wheeler–DeWitt ARC. It carries the exact branch-typed canonical Einstein–source output of WDW-1 through lawful proper-redescription descent without collapsing boundary standing, source ancestry, or physically registered sector data. Its central question is: When two canonical presentations are related by a proper redescription, what must be preserved for them to represent the same authenticated Einstein–source realization rather than an altered physical object? The manuscript constructs the proper-redescription quotient as a global groupoid object, rather than as a naïve orbit set. It establishes spatial-diffeomorphism reduction, an independently certified internal-gauge extension where the relevant occupancy certificates are populated, and regular local quotient/slice structure compatible with the inherited WDW-1 realization. Its central passage is: [ \text{connection-typed canonical Einstein--source realization} \longrightarrow \text{proper-redescription groupoid descent} \longrightarrow \text{representation-stable canonical gravity realization}. ] The descent preserves the complete-history source-realization family, including source and reconstruction ancestry, rather than merely carrying an isolated instantaneous canonical representative. It also retains nonzero boundary charges, flux data, mapping-class information, and registered topological or sector structure. Such data are not silently absorbed into the proper-redescription groupoid as disposable gauge skin. Vacuum and attached Klein–Gordon branches occupy the spatial reduction factor. Nontrivial internal-gauge occupancy is admitted only through independently populated certificates; it is not assumed merely because an internal gauge syntax can be written down. WDW-2 therefore supplies a representation-faithful global descent object together with its regular local quotient/slice family, inherited source and boundary data, and the equivariant lapse-smeared normal-constraint family. This is the exact input carried into WDW-3. It is not a selection of one gauge slice, one fixed lapse, or one preferred canonical representative. The paper does not establish the Hamiltonian self-bracket, full normal characteristic kernel, constrained refoliation theorem, Wheeler–DeWitt operator, anomaly cancellation, physical Hilbert space, or clock interpretation. Those are later ARC obligations. Its load-bearing role is narrower: to ensure that later normal-deformation and quantum-constraint constructions operate on a globally descended, boundary-standing-preserving canonical realization.