A phase magnitude is incomplete until its direction is checked. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A lag is a later copy
The lag case has the same 1 second shift over 8 seconds.
lag=81 cycle
A lead is the opposite direction
The lead case keeps the same magnitude, 1/8 cycle, but the direction label changes.