Profile-Clock Exhaustion and Constraint-Induced Cauchy-Germ Evolution for the Wheeler–DeWitt Constraint

Description Profile-Clock Exhaustion and Constraint-Induced Cauchy-Germ Evolution for the Wheeler–DeWitt Constraint is the seventh paper in the Wheeler–DeWitt ARC. It determines which admissible clock profiles can support a lawful local evolutionary presentation of the renormalized Wheeler–DeWitt constraint realization obtained in WDW‑6. Its central question is: When a surviving Wheeler–DeWitt constraint has no primitive external time, which profile-clock constructions are admissible, and what local Cauchy-germ evolution is induced by the constraint without replacing the constrained system with an independently imposed Schrödinger dynamics? The manuscript exhausts the relevant profile-clock alternatives within its declared comparison class. It distinguishes an admissible relational clock profile from a merely chosen parameter, foliation label, gauge representative, or external time variable. A clock profile has no primitive authority simply by being available in a canonical presentation; it must remain compatible with the inherited constraint structure, proper-redescription descent, refoliation conditions, and physical realization data. Its central passage is: [ \text{renormalized Wheeler--DeWitt realization} \longrightarrow \text{profile-clock exhaustion} \longrightarrow \text{constraint-induced Cauchy-germ evolution}. ] The resulting evolution is a constrained local germ structure: it describes what continuation is available from admissible relational data while preserving the Wheeler–DeWitt constraint. It does not identify the theory with an ordinary externally timed Schrödinger equation, select a preferred global clock, or treat a reduced representative as the standing-bearing physical realization itself. WDW‑7 therefore supplies the temporal and local-evolution input needed by the subsequent covariant–canonical reconciliation and semiclassical-recovery stage. It carries forward the full prior architecture—connection-typed canonical provenance, groupoid-faithful descent, constrained refoliation, joint matter closure, differentiated candidate construction, and quantum constraint survival. The paper does not yet establish global clock-neutral relational descent, final joint constraint-kernel realization, or universality closure. Its load-bearing contribution is narrower: it determines the admissible profile-clock possibilities and the constraint-induced Cauchy-germ evolution available from the realized Wheeler–DeWitt system.