One gamma factor should close both ledgers when the frame setup is fixed. In the
toy faster case, gamma 5/3 stretches 3 s to 5 s and shortens 5 m to 3 m; real
clock-and-rod comparisons still require synchronized frames, calibrated rulers,
alignment control, resolution limits, and uncertainty.
The faster gamma case drives both the longer-time and shorter-length ledgers. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The faster triangle still gives exact time
Gamma 5/3 turns proper time 3 s into lab time 5 s.
3⋅35=5
The same gamma shortens length
The same gamma turns rest length 5 m into moving length 3 m.