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About 2 months ago, I uploaded a fairly long paper (P1) to arXiv and it is currently under review.

Now, I am writing a second paper (P2) on a somewhat different topic. But quite unexpectedly, it seems that to justify a single small step in one section of (P2), I will need a result that I proved in (P1). Unfortunately, this result in (P1) needs several lemmas before it can be proved and the proof of it takes up about 5 pages in (P1).

I have two choices:

1) Do the small step in (P2) by merely citing the statement of the result from my recently uploaded arXiv paper (P1) : But as I mentioned before, the step for which I need this result is a rather small one. Would it really annoy the referee (eventually when I submit this paper) if he/she is referred to 5 pages in a long paper on arXiv merely to justify a small step?

Ideally, I would have liked to keep the papers disjoint, but it does not seem like I can get rid of this one small step in paper (P2).

2) Copy down the entire proof of the required result from (P1), probably in slightly abridged format. But even then, this is likely to add at least 3 pages to the current paper and so it feels unethical (like self plagiarism / salami slicing or something like that).

So what should I do? Are my worries about option 1 (annoying the referee) unfounded? If you were a referee, would you be irritated if I referred you to several pages in a long paper to justify one small step?

Thanks

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    $\begingroup$ This might be a better fit in academia.stackexchange? $\endgroup$
    – Noah Schweber
    Commented May 20, 2015 at 19:29
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    $\begingroup$ As a referee, I would prefer a reference. I would appreciate consistent notation between the two papers, and hopefully some mathematical explanation of why two apparently disjoint papers are not disjoint after all. As I referee, I will also want to know why, if the step is "small", does it take 5 pages. $\endgroup$
    – Boris Bukh
    Commented May 20, 2015 at 19:33
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    $\begingroup$ If I were a referee, I would appreciate having an addendum consisting of a note saying in effect, "I prefer to reference this step, rather than include it", and the five pages justifying the step, so that I the referee don't have to hunt it down. Maybe the referee will help improve on the five pages, or agree with you that the step does not need justifying. If you do a lot to accommodate the referee, the referee might return the favor. $\endgroup$
    – The Masked Avenger
    Commented May 20, 2015 at 19:34
  • $\begingroup$ @TheMaskedAvenger +10 for the last sentence $\endgroup$
    – Yemon Choi
    Commented May 20, 2015 at 19:58
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    $\begingroup$ I'm voting to close this question as off-topic because it belongs on academia.stackexchange.com (and was also asked there: academia.stackexchange.com/questions/45754/…) $\endgroup$
    – Tom Church
    Commented May 21, 2015 at 7:09

1 Answer 1

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If the result is clearly stated in the first paper, there is no reason to reproduce the proof. It does not matter if you are the author of the first paper is not, or if the first paper has been refereed completely or not. However, if you think it is useful or of interest to the reader, you can summarize the main ideas of the argument.

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