Abstract

We distinguish four time-related constructions: a finite-time harmonic relational scalar, an inflaton-clock construction with original slice-harmonic spatial rods and its relational lapse, a prescribed conical incidence parameter with a finite register, and a smooth ramp inserted into a coordinate density. The last object is a regulator, not a dynamical clock.

The distinctions are formulated as statements about domains, defining equations, auxiliary data, and functional dependence. They are supported by explicit calculations. A relational scalar value does not determine the scalar-clock lapse. Original and modified cosmological rods have different first variations, and an explicit compact perturbation makes their quadratic relational lapses different. A fixed density ramp has vanishing field variation and fails the harmonic pure-gauge response test in its transition region. A branch-normal deformation speed depends on the prescribed parametrization and does not determine a matter-defined lapse.

These are classical separation results on the stated kinematic domains. They neither identify the coordinate prescription of Landmark VI with that required by XVI-D nor establish a quantum Ward identity, regulator removal, a continuum evolution, or quantum evolution without an external time. The supplied Family 271 catalogue and its reported Lean scope remain documentary comparisons, not theorem premises.