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A while back, I submitted a paper to a mathematics journal. Since then, I have managed to prove an additional result that I think would improve the paper. If the paper gets rejected, I plan to incorporate the result into the paper and submit again elsewhere. If the journal accepts the paper and asks for revisions, my question is whether it would be acceptable to add the new result when I submit a revised version. The other option is to write up the new result as a separate paper, which may or may not be significant enough for publication.

The reason I ask is that I want to avoid wasting time now. It would be a shame to spend time and effort on incorporating the result into the paper now if I need to remove those changes in the case the paper is accepted. On the other hand, if I can include the result in the current paper, then I don't want to spend time now writing an entirely new paper for this one result.

  • Possible duplicate of Adding a citation after paper is accepted because the answer there is aplicable to a wide range of instances, particularly to this one. – user68958 Feb 14 at 20:58
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    @corey979 I think both 1) adding a new result is pretty different from adding a new citation, and 2) changes after acceptance and changes during revisions are pretty different, so that question differs from that one in two big ways. – Bryan Krause Feb 14 at 21:39
  • @BryanKrause See meta.stackexchange.com/a/10844: "Questions may be duplicates if they have the same (potential) answers". The first paragraph of my answer in the proposed dupe is a general guide for a wide range of such situations: "if you found something that the reviewers didn't ask for, but adding it to the text improves the quality/completeness/etc. of the paper, you definitely should do it". – user68958 Feb 14 at 22:02
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    @corey979 Again, I typically agree with taking a wide view of what duplicates are, but here the questions are too different. I would downvote your answer here and upvote it there: new content should not be added after acceptance unless it dramatically impacts the submitted work, for example, if it shows it is wrong. – Bryan Krause Feb 14 at 22:05
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    @corey979 I also agree with Pete's answer here, because the paper is in revision (and Pete specifically says 'the key point is that the paper is being refereed again'), but your answer on the other question covers all phases of review, which is the part I disagree on for changes like this question asks about (new content) versus changes like the other question asks about (new reference). – Bryan Krause Feb 14 at 22:11
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You can make whatever changes you like in revision. The key point is that the paper is being refereed again. (Maybe the referee isn't paying so much global attention to your paper the second time around. But by the way, maybe the referee wasn't paying so much attention the first time around! There are never any guarantees of that, but you have done your due diligence.)

It is quite common for revised papers to contain many small to moderate changes, including those that were not called for by the referee. If you think about it, it is probably better not just to make precisely the changes asked for -- you are also responsible for your paper as a holistic document, and localized technical changes may necessitate other changes for the sake of unity, coherence and so forth. However, as a referee it is a bit disconcerting to get a paper that has too many changes I have not asked for: at a certain point it begins to feel that I have to referee two papers when I have agreed to referee one. For instance I recall getting a revised paper that was almost 10 pages longer, and I didn't like that much (but I did recommend it for acceptance).

As an author I can think of several cases where I have added significant material to the paper in revision, so it certainly does happen, and at the moment I cannot recall a situation where adding the material seemed to adversely affect the status of the paper. If there is one extra result that you want to put in the paper and its proof takes only a couple of pages, I think you should probably go ahead.

Although I think you'll get away with it fine, whether it is really better to put more theorems into a math paper in revision is a different question that I am a bit too daunted to fully address here. It depends on so many other factors, many of which are cultural. E.g. another answer writes:

I would lean towards publishing a followup paper instead. Does more for you on pub count.

In most parts of pure mathematics having "more papers than theorems" or "more papers than ideas" is looked down upon. If in a certain paper you prove four cognate theorems and then later you try to write up a paper on a fifth cognate theorem, there is a good chance that the journal in which you can publish that little paper is so much worse than the first journal that it doesn't specifically help your career to do so. Whereas if you just appended the fifth theorem in the first paper, you probably wouldn't get any more credit for that either...but at least the fifth theorem would appear in print with little additional trouble on your behalf. I can definitely think of theorems that I have added to papers in this way (not necessarily literally in revision; sometimes just as offshoots of the main project): I proved them so I want to publish them, but I do not always want to play the "How good is this?" game if I don't have to.

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    We once had a job applicant that had about ten times as many papers as all of the other applicants. Almost all of them were in the lowest tier of non-predatory journals - journals that published anything that was valid, correct, unplagiarized mathematics. A few were in somewhat better journals, but none were in first or second-tier journals. This person did not make our shortlist (and, as far as I can tell, never got a permanent position). – Alexander Woo Feb 14 at 21:20
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This is the sort of question to ask the editor. If it is a small change it might be fine. Anything bigger could, perhaps, require another round of review to assure the editor.

Another paper would be a good thing, of course, if you can publish it, perhaps augmenting it with more results to make a more complete whole. But, you need to write it up in any case unless you intend to just abandon it. If it is in the current paper, its significance might not be noticed, of course. But if it is relatively insignificant it might not actually matter to the editor.

You could ask the editor now, which might save some effort. But you could, perhaps, also add it to the next (final?) version if acceptance comes soon. But warn the editor about what you have done so that it is clear. Editors probably don't like surprises.

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This is actually quite common, that by the time the referee report comes you may have a bit more to say. Or the extra bit may come from the revision process itself. It is fine to add it to the paper. Indicate the addition when you send the revised version.

(Quite common: this has happened to many papers I've refereed and to some of mine as well. And I have anecdotal evidence from several colleagues that this is indeed usual.)

Of course, if rather than a bit more you have significant material to add the situation is different: the decision seems now to be whether to write a sequel, to discard the current one, or to thoroughly revise it.

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Small change OK. Big bad.

I would lean towards publishing a followup paper instead. Does more for you on pub count. Let's this one move forward. Plus gives you a little more time to solidify this new finding.

Publish, publish. Don't perish. Don't perish.

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