Abstract

We give a quantum-certificate inventory for four previously separated time-related prescriptions: a harmonic relational scalar, an original-rod scalar-clock lapse, a prescribed incidence register, and a coordinate-density ramp. The ramp remains a prescribed non-clock. No common quantum observable is selected by the labels.

The inventory is supported by self-contained non-implication arguments. A classical operator and its causal commutator do not select a two-point state; a prescribed singularity class does not establish positivity. Individually defined distributions need not have a raw product. Pure-trace evaluations do not determine a three-slot kernel, its microlocal admission, or its free-shell functional. Late source agreement does not determine retarded response. Exact affine repair requires membership in the actual counterterm image, not agreement on finite probes or membership in its closure. Positive formal powers of $\hslash$ cannot cancel a fixed nonzero classical coefficient, and a projected identity is not a full identity.

We also distinguish records from residual instruments and show that even exact subdivision of one finite channel need not select a unique continuous-time evolution. These arguments are audit criteria, not constructions of any native gravitational quantum coefficient.

The original-rod lapse retains its five quantum input obligations; VI's certificate remains RG-open in the supplied record. The reported XVI-Q two-point check is recorded only within its stated prescription and scope. It supplies neither a clock certificate nor a de Sitter state. No inherited characteristic coefficient, quantum evolution without external time, compilation, or downstream quantum-admission conclusion is released.