An important equality that does not erase the separation

This proposition prevents an incorrect universal claim that a kinematical lapse can never equal a scalar-clock lapse. Here equality is obtained by {adding the schedule-defined scalar $S_F$}. It does not identify $S_F$ with the original inflaton clock, supply inflaton-slice rods, or derive the prescribed family from matter dynamics.

The two uses of “lapse” accordingly remain separate: