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Suppose that I put a paper to Arxiv and submit to a journal at the same time. Someone extends my result and clearly cites my paper. This is totally fine. They submit it to a journal. For whatever reason in the review process, their paper is published before mine is accepted. Do I now have to worry that the referee will reject my paper on the grounds that a better result exists, even though they acknowledge that they get the idea from my result?

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    I'd say, don't worry yet. This happens quite often. If the journal you submitted to would've accepted it if that other paper hadn't been published, then they probably still will. Unfortunately if they don't, it could be a little harder to get it published in another journal. – Kimball Jan 16 '15 at 2:48
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On the one hand, referees can reject your paper for all sorts of foolish reasons. I would not if I were refereeing, but that means nothing for some random person with an axe to grind. I wouldn't worry about this scenario too much though, because it would require some relatively extreme timing to happen.

On the other hand, even if it did happen, if people are citing you and you are having an impact, is it really that much of a problem if the paper is "just" in arXiv? Only the most blind and foolish Impact Factor junkies would hold the lack of brand name against you. Also, you will write many papers in your career, and I would be startled if such a situation happened more than once.

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    If a referee did reject your paper for such a reason, saying "The results of this paper are already contained in the paper of Smith et al", wouldn't it be reasonable to appeal to the editor and point out that Smith et al is based on, and cites, your paper? – Nate Eldredge Jan 16 '15 at 3:50
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    @Nate: yes, of course. jakebeal points out that the referee and/or the editor are not guaranteed to be reasonable: alas, he is correct, but the thing about unreasonable people is that you can't reason with them, so it's best not to worry about this in advance. – Pete L. Clark Jan 16 '15 at 3:56
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    On the other hand, I don't agree with the last paragraph: having an arxiv preprint is not at all the same as having a publication, nor should it be. Well, come to think of it, one of my most important papers only appears on the arxiv, which has not stopped it from getting cited (and moreover used in the mathematical sense) by many people, including me. This is not ideal, but indeed life goes on. – Pete L. Clark Jan 16 '15 at 3:58
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    @PeteL.Clark: You are right about arXiv not being the same as a peer-reviewed publication - particularly for hiring / tenure purposes. You never know if this will be the one paper that makes or breaks your tenure decision. (Of course you don't want it to be that close... but still.) – Nate Eldredge Jan 16 '15 at 4:01
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    "Only the most blind and foolish Impact Factor junkies would hold the lack of brand name against you. " Cough... hiring committees, promotion committees, grant funding bodies ... cough... – dorothy Apr 2 '15 at 8:12

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