We are grateful to both referees for their constructive comments that led us to improve the paper.  Our response to the individual points raised follows.

R1: I also found that the authors consider “cohesionless” materials; however, in this argument, they do not use structural analyses (they just extended Pravec et al., 2010). If they want to argue whether or not materials are cohesionless, they have to formulate it in their model. Please note that recent progress in the literature show that materials must have cohesive strength in the present problem; the authors may realize that because of the current assumption of the initial shape, which is an ellipsoid, the theory regarding the equilibrium shape problem can directly be applied to the present problem. However, I believe the point of this paper is different from the argument about if materials are cohesionless; therefore, I do not ask them for this point. I simply suggest that the authors remove the statements regarding “cohesionless” from this paper.
A: We removed the two occurrences of „cohesionless“ (in sections 1 and 6).  Yes, we are aware that it was found that a small cohesion is needed to explain properties of small asteroids, that’s why we comment on it in footnote 12 in section 4.  Our model implicitly assumes negligible cohesion/tensile strength between body’s components that is justified for asteroids of the studied size.  That’s why we had there the word „cohesionless“ in two places, with which we actually meant „effectively cohesionless“ (for our problem with bodies of given size).  But it’s not necessary to look into it in this paper so we just removed the two occurrences of the word.

R1: Lastly, I have a quick comment on the assumption of the bulk density. The authors assume the bulk density to be 2 g/cm^3. I thought this assumption is conservative because the observed spin periods are about 3.6 hr and the derived aspect ratios are about 1.2 – 1.4, according to Section 3. Should it be a lower value? …
A: The observed spin periods are final periods, obtained after the fission and escape of the secondaries.  When corrected for the estimated amount of angular momentum removed from the primary in the process, we obtain an estimate for the initial period (at the moment of fission) of about 3.0 h on average for our studied clusters.  This is about the expected critical spin period for aspect ratio about 1.7 (also seen with the dashed line in Figure 1 in the referee’s report).  This slightly higher aspect ratio than we observe for most cluster primaries is consistent with our model that implicitly assumes that the original body was more elongated as the fissioned material comes from a part of the body most distant from the rotation axis.  As we don’t know details of how exactly the fission process goes, we don’t discuss this point in the present paper.  However, we see that the assumed mean bulk density of 2 g/cm^3 appears to be consistent with the obtained results.

R1: In abstract in page 3: I think “(ibid)” should be the year.
A: Changed to „(2010)“.

R1: “where n and a …” after Equation (1) in page 5: “is” should be “are”.
A: Corrected.

R1: Equations, r <= 5 - 10 R_Hill, v <= 1 - 2 v_esc in page 5: I believe that r and v are normalized. Please describe how to derive them. If these parameters are dimensional, please describes their units.
A: First, we note that we found an error by a factor of 2 in the code calculating the R_Hill and v_esc in our program (used radius instead of diameter in the code by mistake).  We have changed the limits in all the figures to correct ones.  However, we didn’t re-work the plots as the limits of 10-20 R_Hill and 2-4v_esc are still OK for the interpretation of the backward orbit clone integrations; we have added a sentence on it to the 3rd paragraph in section 2.  And to answer the referee’s point: We write in the 3rd paragraph of Section 2 now explicitly that r and v are the physical distance and relative velocity between the asteroid clones.

R1: Definition of d_mean, Page 5: I recommend that the authors show simple review of what this parameter means. I know that Pravec and Vokrouhlick´y (2009) also discuss this parameter. However, showing some examples, e.g., what values effectively indicate the encounter, would be helpful for readers to understand the arguments here.
A: We added two sentences there to the 2nd paragraph of Section 2 with comments on the meaning of d_mean.

R1: The second to the last paragraph in Section 2 in page 6: please define a-dot_max in the sentence (“It was chosen from the range …”) in page 5.
A: We added the reference Vokrouhlický (1999) there.

R1: In Section 2.4: for the two members that did not show orbital convergence, do you think they would depart from other members, instead of the primary?
A: They do show orbital convergence with the primary, but suggest a different time of separation than the other secondaries.

R1: Line 2 in Page 13: please remove either “this” or “2” from “this Section 2”.
A: The sentence was reformulated and the awkward wording disappeared.

R1: The sentence after Equation (4) in page 14: “calculate also” should be “also calculate”.
A: Corrected.

R1: rho‘s in Equations (8) and (9) in page 22: please use a different notation to describe the location of a mass element as rho is already used as the bulk density.
A: We use r for the location of a mass element now.

R1: v_infty,i,j in Equation (12) in page 23: please define that this quantity is the relative velocity of element i with respect to element j when r_i,j becomes infinity.
A: Definition added there.

R1: Definition of omega_c, omega, and omega_j in page 23: Please define these spin rates clearly.
A: For omega_c, now we write there explicitly that it is the critical spin rate.  omega was defined with equation 6 on the previous page.  We added definition of omega_j to equation 12.

R1: Equation (13) in page 24: please explain the right-hand side means.
A: We added a sentence there to the equation (13).

R1: “We also note that …” before Equation (14) in page 24: please remove “that”.
A: Done.

R1: Equation (17) in page 25: although this equation is reasonable, I recommend that the authors describe that the initial body is assumed to be rigid, and therefore the distances between the primary and the secondaries do not change before rotational fission.
A: Our model of the post-fission system actually doesn’t require such assumption on the pre-fission body.

R1: Equation (21) in page 26: please describe that the current study assumes that the initial body is a biaxial ellipsoid, and therefore b_1 = c_1. If not, please define c_1 appropriately.
A: We added that we assume b_1/c_1 = 1.2 to the 4th sentence of the last paragraph of the section 5.  This assumption and its justification was in the Supplementary Information of Pravec et al. (2010), but the referee is right that it needs to be written explicitly in this paper as well.

R1: General: Please define the terms, primary and secondaries. General readers might be concerned which components are either primary or 
secondaries.
A: We added footnote 1 to section 1 defining the terms.

R1: Figures for the histograms of the distribution of encounters: I suggest the authors describe how to this these figures in the captions (at least in Figure 1). For example, for Figure 1, each histogram shows different encounters of the cluster of Irvine. The explanation of the numbers (e.g., 14797, 180233, …) will make the figure clearer. Also, I did not understand what the numbers of the encounters, which are given in the histogram figures, physically means. I believe the authors conduced Monte-Carlo simulations with uncertainties. In page 5, they mention that they integrated a set of geometric clones (500 clones for each asteroids) with … Please clarify.
A: We put description of the things to the 6th paragraph of Section 2.  In the captions of Figs. 1-13, we list the secondaries presented in the individual panels explicitly now.

R1: I have a quick question about Lucascavin (Supplemental Figure 15). The signature of this object looks complex, do you expect this feature results from the shape?
A: Yes.  For a relatively unelongated object (as its amplitudes 0.23-0.30 mag indicate), topographic features can produce such small local maxima.

R2: 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.
A: Indeed, it was a mistyping in the submitted version of the paper; thank you for correction.  Obviously there should have been *normal* instead of *covariance* matrix said in the text.  The original computations were correct, otherwise --as the referee says—the initial conditions would not make any sense.  The text has been corrected now, including reference to Milani and Gronchi (2010).

R2: 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.
A: Now we define the separation time in one before the last paragraph of section 2.  We changed the designation of this quantity to T_{sep}, to indicate its exact meaning.  (We agree with the other comment by the referee below that the term convergence time is used for a different quantity in the literature, so we turned to using T_{sep} now, to be exact and to don’t confuse readers.)

R2: 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?
A: Yes, we consider that these two clusters couldn’t be produced (solely) by rotational fission, they could have been formed by collisions, like larger and older asteroid families, as we mention in the first paragraph of section 6.

R2: 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.
A: The membership of (57738) to the cluster of (18777) appears secure, as we found with our backward orbital integration, as well as by Rosaev and Plavalova (2017).  Note also the very small distance between (18777) and (57738) in the space of mean elements d_mean = 4.24 m/s.

R2: 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).
A: We have added more comments on this to Section 2.11 and we also support the identification of the cluster members by analysis of their orbital clone convergences in secular angle in the Supplementary Information.  We consider the membership fairly secure.  If there are interlopers, they are probably infrequent and only among the smaller members of the cluster, which could produce only a minor error in the mass ratio estimate; see our comments in the new 6th paragraph of Section 3.  See also our further comments below.

R2: 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).
A: Indeed, the referee is right that the full application of the HCM method requires assessment of the minimum number of family members and velocity cutoff (QRL value) from analysis of a population of randomly distributed orbits in the particular zone of the main belt. For instance Milani et al. (2014) provide a *global* value for low inclination zone of the outer main belt and H~14 magnitude cutoff QRL ~ 100 m/s and minimum number of members 17. Here we go to magnitudes up to 17, so it seems that the QRL should have been smaller.

Well, we did not redo the random distribution analysis anew to determine the exact QRL limit. Note also that any global values derived from the whole outer belt zone may have their own issues because of large inhomogeneity of asteroid population (the situation is quite different in very dense families like Themis of Hygiea and somewhere else). In particular, Mandragora family resides at proper a ~ 3.042 au, proper e ~ 0.235 and proper sin i ~ 0.033. This is a region where the local population density of asteroids is rather low (note especially the large eccentricity). This would compensate the decrease in QRL. Just very rough estimate may be as follows: going from H=14 to 17 implies about factor 30 more asteroids, which put in the same volume would decrease the reported QRL by a factor ~ 30^{1/3} ~ 3, i.e., to about 35 m/s. However, lower local density of objects around Mandragora family may then increase the effective  local QRL by a factor of two, say, to ~ 70 m/s.

But more importantly, we actually reported practical detection of the very local QRL near Mandragora family by observing, that up to d_cutoff ~ 75 m/s the family grows only very slowly by accumulating only a small number of asteroids, but at 75 m/s is quickly collapses to the whole background population of bodies. This is in a very good agreement with the rough estimates given above. Our newly associated Mandragora members very near J9/4 required d_cutoff ~ 45-65 m/s, still safe from troubles. Obviously, the final check about their membership in the family consists of rather good convergence to the required
age of the family.

R2: 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.
A: The statistical significance of all the clusters is high.  We have added a comment on it (footnote 5) in section 2 now.

We have added more information and comments to further strenghten or discuss our findings in a few other places in the paper.  We have also performed an analysis of the orbital clone convergences in secular angles for more (8 of the 13) clusters now, added its results to the Supplementary Information (the first 14 pages in the current SI).  We are gratefull to the reviewer who pressed us to improve our paper.