Separate time objects

The following objects are not identified:

1. the continuum coordinate $T$;

2. the finite pointer $T_C={\sum }_k{t}_k{P}_k$;

3. a finite history-event map $\kappa$;

4. a conical slicing parameter;

5. a harmonic relational scalar;

6. an original-rod relational lapse;

7. a prescribed density ramp.

The distinction parallels XIX-A CheungXIX. For example, the scalar $T$ is harmonic for both constant-lapse metrics above, while

depends on $N$. The scalar profile alone does not determine the lapse.

For the unit-lapse static history events chosen here, $t_k-t_j$ equals their geometric static proper-time interval. That equality follows from the supplied metric and event map. It is not inferred from the numerical code, and the individual code does not determine a proper-time origin.