  Transit surveys have revealed a significant population of compact
multi-planet systems, containing several sub-Neptune-mass planets on close-in,
tightly-packed orbits. These systems are thought to have formed through a final
phase of giant impacts, which would tend to leave systems close to the edge of
stability. Here, we assess this hypothesis, comparing observed eccentricities
in systems exhibiting transit-timing variations (TTVs), with the maximum
eccentricities compatible with long-term stability. We use the machine-learning
classifier SPOCK (Tamayo et al. 2020) to rapidly classify the stability of
numerous initial configurations and hence determine these stability limits.
While previous studies have argued that multi-planet systems are often
maximally packed, in the sense that they could not host any additional planets,
we find that the existing planets in these systems have measured eccentricities
below the limits allowed by stability by a factor of 2--10. We compare these
results against predictions from the giant impact theory of planet formation,
derived from both $N$-body integrations and theoretical expectations that in
the absence of dissipation, the orbits of such planets should be distributed
uniformly throughout the phase space volume allowed by stability. We find that
the observed systems have systematically lower eccentricities than this
scenario predicts, with a median eccentricity about 4 times lower than
predicted. These findings suggest that if such systems formed through giant
impacts, then some dissipation must occur to damp their eccentricities. This
may take place during formation, perhaps through interactions with the natal
gas disk or a leftover population of planetesimals, or over longer timescales
through the coupling of tidal and secular processes.
