Configuration-Space Differentiation and the Constraint-Native Wheeler–DeWitt Candidate Family

Description Configuration-Space Differentiation and the Constraint-Native Wheeler–DeWitt Candidate Family is the fifth paper in the Wheeler–DeWitt ARC. It carries the source-attached, jointly constrained classical interior established by WDW‑4 across the next type boundary: to separately typed, regulator-indexed quantum-constraint candidate families. Its central question is: Given the completed WDW‑4 classical gravity–matter constraint interior, what configuration carriers, differential structures, representations, and constraint actions can be constructed without silently claiming quantum closure that has not yet been earned? The manuscript constructs two distinct branches: a metric–scalar/clock core; and a torsion-free tetrad–Standard-Model extension incorporating spin, gauge, Higgs, and chiral-fermion structure. For each branch, it supplies local Sobolev configuration carriers; proper-redescription action and local descent; tangent, cotangent, and canonical normalization data; separating test algebras; independently defined first and second Fréchet differentials; regulated Hessian contractions; algebraic CCR/CAR representation seeds; and complete linear and Hamiltonian constraint actions on one algebraically invariant test domain. Its central passage is: [ \text{joint WDW-4 classical constraint interior} \longrightarrow \text{configuration-space differentiation and regulated representations} \longrightarrow \text{constraint-native Wheeler--DeWitt candidate families}. ] The paper does not insert a formal Wheeler–DeWitt expression as a primitive. Coincident second-order functional contractions are replaced by declared positive-regulator traces, and the resulting constraint families are classified within their stated compatibility class. Formal joint solutions are considered only in the algebraic dual, with no claim that this already provides a physical state space. The endpoint is deliberately exact: WDW‑5 reaches the regulator-indexed algebraic candidate level. It does not prove regulator removal, quantum commutator closure or anomaly freedom, a Hilbert-space realization, physical inner product, nonzero physical states, rigging map, relational observables, or a separating observable algebra. Those are the expressly exported burdens of WDW‑6. WDW‑5 therefore supplies a source-faithful and technically typed quantum candidate input to the next ARC stage. It ensures that quantum-survival analysis begins from a jointly occupied gravity–matter configuration structure with defined differential, representation, and constraint data—not from an unregulated formal functional equation.