Abstract

We record the exact boundary of a programme separating a harmonic relational scalar, an original-rod scalar-clock lapse, a prescribed incidence register, and a coordinate-density ramp. The first three stages concern classical prescriptions and finite interfaces; the fourth inventories unclosed quantum inputs. This final note neither identifies their targets nor completes a quantum or continuum construction.

The boundary is supported by self-contained comparison arguments. Fixed density multiplication and fixed convolution are different operations. A density ramp can fail the first harmonic pure-gauge response test in its transition region without contradicting a plateau-restricted identity. Pure-trace evaluations have a smooth kernel blind sector. Agreement away from an extension locus does not select an extension, and finite normal order does not imply a finite-dimensional ambiguity. Scheduled channel support does not select a metric, clock calibration, or continuous-time generator. Even exactly consistent subdivisions of one finite channel can have different continuous-time limits. Finally, localization and smoothing coefficients do not transfer without a specified comparison map and parameter identification.

The remaining claims are version-qualified documentary boundaries: VI's RG-open certificate, the five quantum inputs of the original-rod lapse, the native incidence continuum realization, the complete characteristic map, insertion and route obligations, and physical or holographic interpretation. External catalogue entries are not theorem premises. No inherited characteristic quantum coefficient, quantum evolution without external time, compilation, independent predecessor verification, or full spacetime emergence is released.