  Filming atoms in motion with sub-atomic spatiotemporal resolution is one of
the distinguished scientific endeavors of our time. Newly emerging X-ray laser
facilities are the most likely candidates to enable such a detailed gazing of
atoms due to their angstrom-level radiation wavelength. To provide the
necessary temporal resolution, numerous mode-locked lasers must be synchronized
with ultra-high precision across kilometer-distances. Here, we demonstrate a
metronome synchronizing a network of pulsed-lasers operating at different
center wavelengths and different repetition rates over 4.7-km distance. The
network achieves a record-low timing drift of 0.6 fs RMS measured with 2-Hz
sampling over 40 h. Short-term stability measurements show an out-of-loop
timing jitter of only 1.3 fs RMS integrated from 1 Hz to 1 MHz. To validate the
network performance, we present a comprehensive noise analysis based on the
feedback flow between the setup elements. Our analysis identifies nine
uncorrelated noise sources, out of which the slave laser's inherent jitter
dominates with 1.26 fs RMS. This suggests that the timing precision of the
network is not limited by the synchronization technique, and so could be much
further improved by developing lasers with lower inherent noise.
