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What would you do/have you done in such a situation?

  1. Hand out the improvement for free in your report

  2. Wait until the result is published and then submit elsewhere

  3. Inform the editor about the situation and ask for advice

The paper is not posted publicly so contacting the authors directly informing them and asking what they want to do is out of the question.

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    $\begingroup$ Perhaps not the same, but these questions on Academia Stack Exchange seem related: A manuscript I refereed gave me an idea for a paper, not sure how to proceed and How to use results/ideas from a paper I reviewed? $\endgroup$ – Martin Sleziak Dec 9 '18 at 16:15
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    $\begingroup$ I invariably do #1. Usually that is reciprocated with an offer of co-authorship, which I accept or decline based on the circumstances. $\endgroup$ – fedja Dec 9 '18 at 16:15
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    $\begingroup$ This very much depends on the nature of the improvement, and the people involved. I can imagine myself doing all three, in different circumstances. $\endgroup$ – Mark Grant Dec 9 '18 at 16:27
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    $\begingroup$ This happened to a paper I submitted awhile ago. The referring report came out with a simpler proof and and an improvement on the result. I felt that the improvements were substantial, and I asked the editor to ask the referee whether they would accept to coauthor the paper. They did (it turned out the improvement was a joint effort between 2 referees), and the paper appeared shortly after with three authors. In my mind this was the most fair outcome. $\endgroup$ – user129564 Dec 9 '18 at 17:51
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    $\begingroup$ I don't see how I would develop a professional relationship given that I am anonymous or do you mean with the editor? $\endgroup$ – Hercule Poirot Dec 10 '18 at 8:34
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Option (1) is definitely the professional course of action in this case. As pointed out in the remarks, it is likely to lead to an offer of co-authorship from the original author, but that is purely within the author's discretion. If you feel that your improvement is really substantial and you are worried about credit you can try to increase the chances of co-authorship by asking the editor to put you in contact with the author (after explaining the situation to the editor). You may then discuss this with the author directly and suggest co-authorship, a situation in which the author is more likely to accept (but they still may insist to refuse, in which case you should give them the idea "for free"). If your improvement is sufficiently significant and novel that not getting credit for it seems an unacceptable injustice, then what you can do is wait for the paper to be published (or accepted and online) and then write to the author with your idea of improvement and suggest co-authorship for a second paper. Here of course if they refuse you can publish alone. In any case, you should not submit your own paper without giving the original author a chance of co-authorship. That would be rather unprofessional.

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Just do (1), and pat yourself on the back!

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My advise: don't do 3) in any case. It is up to you to decide, not the editor. The rest depends on the paper and on the improvement.

  1. Would you recommend to accept the paper as is? Suppose the answer is yes. Now imagine that you see this paper published, and you see how to make an improvement. Would you publish this improvement as a separate paper of your own? If yes, then do 2). If not, do 1).

  2. You think the paper in its present state is not worth publishing but your improvement will make it worth. Then do 1). Then it is likely that the author of the paper will propose you joint authorship. And you may agree or not.

  3. If you think that the paper does not deserve to be published (with the improvement or without). Then recommend to reject and do nothing else.

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  • $\begingroup$ Thanks this is quite helpful, my feeling is that it is somewhere between your 1. and 2. so my 1) is the best option forward. $\endgroup$ – Hercule Poirot Dec 10 '18 at 8:33
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    $\begingroup$ Asking for advice to the editor does not mean that the editor decides... $\endgroup$ – YCor Dec 10 '18 at 23:39
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If you have tenure, or even a tenure-track job, I'd definitely advise just doing 1. If you're in a less secure job position and the improved result is really good, I'd suggest doing roughly 3. That is you tell the editor "I think I can significantly improve the main result, do you think it would be appropriate for me to suggest this improvement non-anonymously to the authors?

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    $\begingroup$ that makes sense, I am in a secure job, I will go for 1) $\endgroup$ – Hercule Poirot Dec 10 '18 at 22:20

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