First let me point out two small but very disturbing mistakes, both
appearing in the middle of page 6: the Gaussian probability density
function (PDF) appears to be computed by using a quadratic form with
the COVARIANCE matrix (in the exponent). As you can find in any
textbook (just as an example, Milani and Gronchi 2010, section 5.7),
the PDF is computed with the NORMAL matrix, which by the way is also
provided by the AstDyS site precisely for this purpose. I hope this is
just a typo, otherwise the swarms of "clones" used in rest of the paper
would be all wrong. 

Few lines below, the symbol T_{conv} appears from nowhere, never being
defined. It is not that obvious what is meant by this symbol,
especially taking into account that in Table 1 each individual cluster
member appears to have its own T_{conv}. Please give a very formal
defintion of this quantity and how it is computed.

This paper contains a significant amount of data on small clusters of
asteroids, close in mean elements space. 13 such clusters are
presented and the membership list, distances in a suitable
5-dimensional metric, absolute magnitudes and an estimated epoch for
the separation are given (table 1); also an estimate of the mass
combined ratio of the presumed fragments and rotation periods (Table 2
and Figure 15). All this is valuable for the purpose of studying this
phenomenon, and in the Section 4 and 5 the authors propose a
comprehensive physical model for rotational fission, then compare it
with the data, concluding that this model can explain 11 out of 13
cases. The two exceptions are the clusters of (1877) Hobson and
(222280) Mandragora.

To express the doubts this work leaves unanswerd let us start from
these two counterexamples: (18777) and (22280). Are these examples of
another possible mechanism of formation? Or rather, are they examples
that the statistical reliability of the clustering procedure is not
that high? Indeed, if the list of members was changed, the mass ratios
of table 2 could be quite different. E.g., if the (1877) cluster does
not contain (57738), then the mass ratio would be quite different. If
the membership of (22280) was less numerous, in particular taking into
account some difficulties in the use of mean elements due to the 9/4
resonance with Jupiter, then the mass ratio could be lower. Since it
turns out hta I am one of the authors of the mean elements published
in the AstDyS site and used in this paper, please note that these data
came with a flag "Quality Code for Mean elements (QCM)", which is 0 for
good values, and has value 4 (meaning very bad) both for (22280) and
(324154).

In particular in discussing the (22280) cluster case, section 2.11,
the authors claim they have used the HCM method. In fact, they have
used only a portion of this method selected by themselves, that is the
algorithm to cluster asteroids up to a given distance, but not the
method, contained in the original formulation of HCM (Zappala' et
a. 1990, 1994) to stop the clustering at some well determined distance
limit. A distance limit of 100 m/s is by far too large, especially to
look for a supposed recent family, formed < 1 My ago, and with parent
bodies of the order of 10 km in diameter (thus this difference limit
is large with respect to the escape velocity from the parent body).

More generally, and this comment applies to essentially all proposed
clusters, I appreciate that the authors give an explicit list of the
membership proposed for the clusters, but I have not understood what
is the statistical criterion to assess the probability that such a
cluster exists, and has actualy the membership stated. 

I am aware that the membership is confirmed by computing T_{conv}, but
then I am lost because I do not know what this quantity is. What I
empirically find from table 1 is that in the same cluster there are
many different values, sometimes with overlapping errorr bars, some
times incompatible. Then, why is the existence of these different
values a confirmation of the "reality" of the cluster? Taking example
from the too often misquoted HCM method, in a complicated situation
such as this a good strategy is to make up a Montecarlo simulation
indicating that some clusterings are either too large or too tight to
occur at random. But if you allow for a different age for each
splitting event, you do not have a coincidence of many ages, then what
is there in the clusterings which would not occur at random? In work
by other authors on the subjects of recent asteroid families,
"convergence" is defined as small differences of some quantities (such
as longitudes of nodes and perihelia) for many members at one and the
same time.

In conclusion, this paper contains useful information, but requires
some additional work to be able to claim that the clusters both exists
and are well defined in their composition. Then also the
correspondence between the cluster data and the rotational fission
model, although I accept that Figure 15 suggests a significant link between the two, becomes unsure.

Andrea Milani, Pisa 10 April 2017