Question and exact kind of conclusion

The question is what remains outside the clock-separation programme after XIX-A, XIX-B, XIX-C, and XIX-D XIXA,XIXB,XIXC,XIXD. The answer is a boundary inventory, supplemented by explicit non-determination arguments. It is not a new theorem that every future clock identification, quantum construction, or spacetime realization is impossible.

The four entries remain

They denote, respectively:

1. a scalar dressed by a specified harmonic-coordinate map;

2. a matter-clock lapse pulled back using the original clock-slice harmonic spatial rods;

3. a prescribed incidence parameter together with finite reading and update interfaces;

4. a prescribed profile placed in a coordinate density.

These are four time-related entries, not four certified physical or quantum clocks. The fourth is the named non-clock.

The motivating manuscript records are Cheung's VI, VIII-A/B/C, X-A, X-A-conv, Em02-E, and the analytic and operational comparisons specified below CheungVI,CheungVIIIA,CheungVIIIB,CheungVIIIC, CheungXA,CheungXAconv,CheungEm02E. Their equations, domains, gauges, auxiliary inputs, and releases are not identified by their names.

Relational-coordinate constructions provide established context BFHPR. Quantum fields on a classical background and their states, composites, and products provide another context HW,BF. Neither context automatically supplies the particular quantum inputs or comparisons required by this programme.