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Suppose I finished work on a manuscript and submitted it to a journal. After X weeks, I suddenly realized I can prove one of the conjectures I left open in the concluding section. It seems that X is small enough (e.g. 1) so that nothing visible has happened to my submission yet.

The proof is not long, and wouldn't be important enough to merit its own paper. Will it reflect badly on me if I contact the managing editor to have the current submitted version updated? The smaller X is, the less annoyed people would probably be. I could just submit to arxiv, but I would like to make the manuscript stronger, and don't have results scattered around giving a hasty impression either. Or is there another solution I'm overlooking?

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    Probably better to wait for the reviewer comments and incorporate everything in one go. It's a pretty safe bet considering how uncommon it is to get an accept straight away, at least in my field. Secondly, considering you see another proof only 1 week after submission already induces a hasty impression. – Marc Claesen Jan 30 '15 at 23:47
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As Marc says in his comment, the best thing to do is probably to incorporate the new proof into your revision, after you get reviewer feedback. A small extension not worth its own paper is unlikely to make a difference between reject and revise. If you send it now, it may annoy the editor and reviewers. Also, the reviewers will likely be just fine with more new material you add in revision.

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  • Out of curiosity: how much material can you actually add to your work after you get the reviewer feedback? If the addition is substantial enough, shouldn't it be reviewed again? Does the editor even like such behaviour? Does it happen that the author adds in stuff, and the reviewers look at the additions again? I'd think that it's good for the paper and the scientific community the stronger the paper is, but I can see this might be a little messy... – mrm Mar 22 '15 at 12:50
  • For a journal process, you can add quite a lot, just declare it in your response letter. The editor will decide whether it needs to be sent to the reviewers again or not. Speaking from my experience as an editor, adding material that strengthens a paper is pretty much always welcome, since it's good for everybody involved. – jakebeal Mar 22 '15 at 13:39

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