  Dawson and Murray-Clay (2012) pointed out that the inner part of the cold
population in the Kuiper belt (that with semi major axis a<43.5 AU) has orbital
eccentricities significantly smaller than the limit imposed by stability
constraints. Here, we confirm their result by looking at the orbital
distribution and stability properties in proper element space. We show that the
observed distribution could have been produced by the slow sweeping of the 4/7
mean motion resonance with Neptune that accompanied the end of Neptune's
migration process. The orbital distribution of the hot Kuiper belt is not
significantly affected in this process, for the reasons discussed in the main
text. Therefore, the peculiar eccentricity distribution of the inner cold
population can not be unequivocally interpreted as evidence that the cold
population formed in-situ and was only moderately excited in eccentricity; it
can simply be the signature of Neptune's radial motion, starting from a
moderately eccentric orbit. We discuss how this agrees with a scenario of giant
planet evolution following a dynamical instability and, possibly, with the
radial transport of the cold population.
