----- Comments from reviewer 1 -----

the scientific content of the paper is extremely interesting. The Belle-II TOP detector is state-of-the-art in imaging Cherenkov detection. However the paper has several problems. The English is poor throughout\
, it seems to become worse as the paper goes on. It would benefit from a native English speaker to re-draft it. I also found a significant amount of non-scientific language. The use of first person plural is no\
t to my taste, but that is a question of style I guess. Sadly, I found that the lack of written quality distracted from what is an excellent scientific achievement from the TOP collaboration.

Firstly, the paper is not all the author's own work. Whether he chooses to be a single author is a decision between him and the TOP collaboration, however the author *must* acknowledge the work of others. This \
would be best indicated "On behalf of the Belle-II TOP collaboration" (or equivalent) directly under his name. Less preferred is to thank the rest of the Collaboration under a final section "Acknowledgements" \
(which will need to be included anyway). I just hope this paper has been blessed by the rest of the collaboration.

The comments below are not exhaustive, and demonstrate the scale of the problem.
[Follows a list of style and grammar corrections]

Include acknowledgements. Thank appropriate funding agency.
Much of the final paragraph is repetion of what's gone before in the bullet points. Indeed, the paper might benefit from a "Summary and Future Plans" section (but keeping within the page limit), where any repet\
ition would be part of the summary. I have to say, for me, the paper just fizzled out ...

In summary, as a referee, I am disappointed that I had to make so many corrections on behalf of the author.


----- Answers to reviewer 1 ------

We thank the revewer for the very thorough revision of the paper style, wording and grammar.
We implemented all the suggested style changes.

We have modified the last part of the paper that was indeed repeating itself, leaving only the pure description of the calibrations in the bullet-point list
and moving all the description of how we coped with the small statistics available and how this affected the calibraiton percision to the very end of the paper.

We did not add any acknowledgements, as the would require almost one whole page and it's not requered by the collaboration pubblication bylaws.

We would finally like to reassure the reviewer that the paper was made availabel to the collaboration before the submission and went though the
internal revision process required by the Collaboration.




----- Comments from reviewer 2 ------

First results from Phase II of the TOP counter of Belle II are welcome and a very interesting reading. Moreover, the article is clear, the English correct and easy to read.

I have found two typing errors:
Line 151: "to small to...", change in "too small to...";
Line 170: "the the relative", change in "the relative".

One thing this reviewer regrets, and it is the reason of the minor revision, is that "what the expectations are" is missing; conversely, "what the performance degradations amount to"?

The author mentions this in at least two places: lines, 110 to 117 and lines 189 to 194, but the reader is left with the information that a performance degradation is present (and fully explained according to t\
he author), not having an idea of what, how much and where the degradation is. (possibly reading the whole TOP publications, this would come clear …)

Therefore, the request would be to add a few lines quantifying this or at least giving a comparison between expected and measured.



----- Answers to reviewer 2 ------

We thank the reviewer, and we understand the request of the rewiever for more quantitative statements. However, our paper reports about the very first findings. By the time of the writing we didn't have expesin\
ve measurements of the identification efficiency. We have nevertheless re-phrased out statement about the effieicny and fake rate measurement, that now reads:

"Overall, the identification efficiencies for proton (not presented in this paper), kaon and pion measured in the commissioning run are approximately $10\%$ below the Montecarlo expectations. Similar discrepanc\
ies are also present in the fake-rate measurement, which are higher than the design value. Numerous studies are being performed to better understand these differences and reduce or eliminate them, as discussed \
in the next section."

And we have added earlier in the paper a reminder of the expected performances, with a corresponding reference:
"MC simulations show that a kaon identification efficiency of $90\%$ can be achieved while keeping the pion fake rate below $5\%$ in the momentum region between $0.5$ and $2$ GeV/c"

----- Comments from reviewer 1 -----

The paper is now considerably more lucid. So I am now able to see "the wood for the trees".
I repeat that I think this is an important paper, describing the operation of a state-of-the-art detector.
However there are a few residual comments, mainly English.
My major comment is Figure 2 (bottom pane). In truth, I cannot see what this figure brings - it adds very little to the point of the discussion. Indeed, it brings more questions than answers :
- Is it the same event as the panes above it? This should be stated. If it isn't the same event, then I *really* don't get the point of it.
- Why is the "IP" (which by the way is not defined) not at (0,0) ? Is this an artifact of the Belle-II coordinate system? Needs clarifying.
- The top panes are very nice. But please explain why there are *two* expectation bands on the left hand and centre plots ? Why is there only one band for the protons? Please explain in the main text or the caption.


Now the remaining English corrections:

Line 25 by -> of
Line 30 long -> wide
Fig 2 caption : of same -> of the same
Line 46 are -> is
Line 46 Cherenkov -> the Cherenkov
Line 51 channel -> channels
Line 52 introduce a space between comma and K -> \pi, K [no big deal]
Line 85 of -> to
Line 119 likelihoods -> likelihood
Line 121 with the either -> with either
Line 122 hypotheses -> hypothesis
Line 125. Clarify that this is the *relative* efficiency (not absolute)
Line 132 I would advise replacing "points to" to "suggests" [because it reads as data-points.]
Line 172 equal -> equal to
Line 180 of di-muon -> of the di-muon
Line 188. There is a sentence in the text which is completely out of context. "The geometrical alignment has not been performed." What does that mean ? At the very least the sentence should be blended in to make some context.
Line 191 on an typical -> for a typical

I still think the paper ends in a very awkward and abrupt way. But this is at the author's disgression I guess ...



----- Detailed answers to reviewer 1 ------

1) Comments about Figure 2

The structures of the PDF strongly depend on the impact point and direction of the particle on the TOP active volume. For this reaosn we decided to add the bottom panel, that of course is the same event as the one shown in the PDF panels. However, we recognize that is overwhelming the reader with more information than they can digest, and it's of limited interest if only one event is shown. We have removed it.
The reason why the IP projection does not fall in the middel fo the TOP polar angular coverage is that, as a consequence of the asymmetric beam energies, the events are boosted and the detector is not symmetric to optimize physics acceptance. As such one cannot assume forward/backward symmetry respect to the interaction point (IP) for the TOP either.
Concerning the upper panels, we have indeed chosen a very peculiar event in which the small difference between the Cherenkov angles for kaon and proton produce a major difference in the PDF pattern. This is not a typical case, and we have decided to replace the event with a more conventional one.


2) Line 30 long -> wide

The prism is 10 cm in the z direction, i.e. along the beam axis, that is defined as the lenght of the module.
We use the term "wide" to refer to the transverse dimensions of the TOP, i.e. along the azimutal direction.
This is the same convention depicted in Fig. 1

3) Line 188. There is a sentence in the text which is completely out of context. "The geometrical alignment has not been performed." What does that mean ? At the very least the sentence should be blended in to make some context.

We removed that sentence, since we already mentioned that the geometrical alignment did not produce realiable results.


4) I still think the paper ends in a very awkward and abrupt way. But this is at the author's disgression I guess ...

We added a section describing the improvements we made before the restart of the data taking in 2019


Finally, Aìall the English corrections have been implemented