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I was given a paper to peer review. A result of that paper has been obtained with some extrapolation trick and so they present it as highly plausible conjecture.

It turns out that me and another collaborator computed the exact same thing (for other reasons) in a work that is still unpublished and we used a method that is rigorous. Our results match so in principle I could prove their conjecture.

Now there are a few things I could do, and I'd like some opinions from you:

  1. Don't say anything. When our paper comes out I will cite them and say that we prove their conjecture. This is ok, but it itches me a bit to recommend the publication of a result claimed as merely a conjecture when I know it to be true.
  2. Say in the report "hey, by the way, you could prove your result by doing this. Please do it." However it is a hard computation to set up and I would just make them waste time. Also, I would need to ask my collaborator's permission on this.
  3. Say in the report "hey, by the way, I have unpublished work that proves your conjecture, so great news." But I don't know what that would accomplish.

I'm obviously leaning towards 1. but maybe some of you have even better ideas.

BlueElephant
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    I'm having trouble resolving the dilemma, to be honest, but let me complicate it a bit by noting that the authors may already have a follow up paper in process. – Buffy Jan 02 '21 at 17:50
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    A fourth option is to withdraw from the review, but tell the editor why. Or at least, ask the editor's advice. – Buffy Jan 02 '21 at 17:55
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    A somewhat similar situation: During review, I found a superior solution. What now? – Anyon Jan 02 '21 at 18:00
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    I think it was unwise that you were reviewing the work of someone who is looking into the same question. As it was a conclusion of the research it must have been mentioned in the abstract and you'd have been wise to leave it. You were "too close" to resist the moral hazards that might occur - and unfortunately it did. Best thing now is to step back, explain the conflict honestly to the editor and beg leave to recuse yourself. This of course leaves you free to publish your own complete proof of their extrapolated assertion. – Trunk Jan 03 '21 at 15:11
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    @Trunk to put this into a clearer context: the thing that they conjecture and that we prove is not the entire content of their paper, and neither of ours. It's just a preliminary result needed to do other stuff. This means also that it was not explained in a level of detail in the abstract for me to realize this issue earlier. – BlueElephant Jan 03 '21 at 15:19
  • I see. Still and all, it might be safer to pull out. As you'd already planned to publish (perhaps as an inclusion in a bigger work, perhaps as a "letter" ) your proof, you can still do that with integrity provided you don't take it in some direction suggested by the authors of the reviewed paper. But approaching the author directly or indirectly ahead of publishing your own paper would not be good IMHO for the integrity of the peer-review process unless it is one of these "open" things. Neither should it be good for your own self-esteem to so act. After both are published - che sera, sera. – Trunk Jan 03 '21 at 21:39
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    "it itches me a bit to recommend the publication of a result claimed as merely a conjecture when I know it to be true" just pointing out, this is a red herring, and definitely not the right way to think about this. Your job as a reviewer in this context is to judge whether this is a useful, non-trivial contribution in relation to the extant literature, not in relation to some future superior literature that you or somebody else may or may not personally get round to publishing at some point in time; this is regardless of how much ''better' or 'solid' that future imaginary publication may be. – Tasos Papastylianou Jan 04 '21 at 10:14
  • @TasosPapastylianou Good point, I agree – BlueElephant Jan 04 '21 at 11:30
  • @Trunk Makes sense – BlueElephant Jan 04 '21 at 11:32
  • to add to TasosPapastylianou's point, you could literally die the day after you submitted your review and this paper could stay a conjecture for a hundred more years before another BlueElephant is born to prove it. As long as you are inclined to recommend publication, you should be in the clear, but if you'd be inclined to ask for a major revision or a rejection, it will be hard to prove that your resolution was honest and not because of competing interests. – Andrei Jan 05 '21 at 18:49
  • @Andrei I hope I'll still be around to publish my ongoing papers ^^'. Jokes aside, I submitted the referee report and recommended for publication. – BlueElephant Jan 16 '21 at 09:59

4 Answers4

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I was once in a very similar situation, proving a conjecture from a paper that I was refereeing. (But, unlike you, I hadn't worked on it before, and I didn't have a coauthor.) I essentially left the situation up to the editor. I sent her my proof along with my report on the paper. With my permission, she shared this information with the authors. It turned out that, in the meantime, someone else had also proved the conjecture, by a quite different method. He and I ended up publishing a joint paper that combined and extended both of our methods.

One warning, based on this experience: Don't get so excited about this that you overlook an error elsewhere in the paper you're refereeing.

Andreas Blass
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Honestly, I do not see a problem here. My advice is to focus on your duties as a referee, i.e. check if the manuscript deals with the hypotheses appropriately, if the methods are suited for their purpose etc. If the authors properly build upon the currently publicly available knowledge, you have no reason to critisize this aspect of the paper. As you describe it, the authors obtained a correct result and used it in their reasoning. They may have used another method than you, but that is totally okay. So primarily judge the manuscript in itself without thinking too much about your own, unpublished work. This way, you also reduce the conflict of interest issue.

Conflicts of interest to some degree are inherent to the peer review process. You have to be an expert in the field to assess the work, so it is not unlikely that you have some own more or less related work. This in itself is nothing to worry about. If you feel unsure whether in your case the overlap is too big and you cannot guarantee that you assess the manuscript on a neutral basis, explain to the editor and let her/him decide.

About contacting the authors (via the editor!) and a possible cooperation: Ask yourself what you want. In my opinion, you are not obliged to do anything into this direction (although you could, as pointed out in the other answers). As a referee, you should remain as neutral in the process as sensible. Just imagine what would be the situation if somebody else had got the manuscript for review. You would then build upon the work in question in your own future paper, like you obviously should. That you got the manuscript for review should not necessarily make any difference.

Snijderfrey
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    I would say the fact OP has the proof in their back pocket is a good indication they're the right person to be reviewing this paper! – corsiKa Jan 04 '21 at 20:48
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    @corsiKa it is more of an indication that there might be a conflict of interests. Just imagine if two competing people always get each other's papers. I'm not saying that they would, but they could ask for major revisions only to advance their personal interest of getting more time to work on own solution, instead of their interest of providing honest feedback. – Andrei Jan 05 '21 at 18:42
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In the best of all possible scientific worlds I think the proper outcome might be a joint paper. That would make it easier for people to find out the latest news on the topic in a single place.

Whether that's appropriate or possible in this instance requires much more information about the technical details and the people involved than you can provide here.

I agree with the consensus from other comments and answers that you begin figuring out what to do by contacting the editor.

Ethan Bolker
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Go for option 1, but in addition (when sending the report) tell the editor that you have a proof of the conjecture in an upcoming work of yours. (Or inform the editor immediately, if you will still take some time to prepare the report, in case you want to avoid the impression you only started working on this once you received the paper.)

Of course, if you feel comfortable revealing your identity you can also email the authors once you have finished the review. (However, note that this might be problematic if you get the paper again in a second round of refereeing since then you are no longer anonymous, which might bias the way in which you write the report.) And if you feel uncomfortable with the situation, withdraw from the refereeing.

Finally, if in doubt, you can always check with the editor. It's their job.

user151413
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    No, don't contact the authors. Don't break blind refereeing. – Buffy Jan 02 '21 at 21:11
  • @Buffy I don't think it is forbidden. (Is it?) Or do you just feel it is wrong? If the OP feels they can provide a fair review even when revealing their identity, why not? I'd say bling refereeing means the possibility of staying anonymous, not the obligation. (Some journals - e.g SciPost - have the option for referees to reveal their identity. I certainly would not feel it is problematic if the referee feels they can provide a fair report even when disclosing their identity.) – user151413 Jan 02 '21 at 21:55
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    The expectation is that you don't unless you have permission. Use the editor as a go-between in normal cases. – Buffy Jan 02 '21 at 22:01
  • @Buffy Is there any source for that? – user151413 Jan 02 '21 at 22:28
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    @user151413 https://academia.stackexchange.com/q/9523/17254 – Anyon Jan 02 '21 at 23:05
  • @Anyon Thanks. Yet, there are two issues with the question/answers: First, I would be interested to see if there are any official rules from journals which forbid that or whether anonymity is rather an offer to the reviewer. Second, the question you link is about requesting clarification from the authors. My question is rather: Is there anything wrong with telling the authors "hey guys, I reviewed your paper (and by the way, I can prove X)". – user151413 Jan 02 '21 at 23:10
  • In my experiencing communicating via the editor is a norm, not an explicit rule, but it is a fairly general norm. (For example, when I want to waive my anonymity as a reviewer, I add this as a comment to the editor, rather than taking it on myself to break anonymity by contacting the authors directly.) – Ben Bolker Jan 03 '21 at 00:37
  • @BenBolker I agree it is the norm. My question here is really whether there is any evidence where journals explicitly forbit it (just like they explicitly forbit sending the paper to two journals, or without the permission of a coauthor, and so on), or whether this is more a "gentemen's agreement", like good manners. I think the situation described in the question potentially backs up such action. In any case, not that this is not what my primary answer suggests! – user151413 Jan 03 '21 at 01:12
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    Would make a reasonable new question, if you want to bother. I have never come across any such explicit rules (I do read editorial policies carefully sometimes, but certainly not always) – Ben Bolker Jan 03 '21 at 01:33
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    @user151413 Probably not all journals have such official rules, but e.g. American Physical Society requests that: "When you are reviewing a manuscript, please do not initiate discussions with the author(s); instead, please contact the editors with your inquiry." COPE's Ethical Guidelines for Peer Reviewers states more strongly that, during review, peer reviewers should "not contact the authors directly without the permission of the journal". – Anyon Jan 03 '21 at 04:14
  • The journal for which I am reviewing has a policy that all communications should go through their online portal, which sends my messages to the editorial office. For what is worth, there is a journal where referees can be made public, if they wish, but this is not it. – BlueElephant Jan 03 '21 at 10:47
  • @Anyon Thanks for looking that up. However, this is not what I am thinking of: I am rather wondering if there is any rule against contacting the authors after (or independently) of the review, saying "Hi, I just reviewed your paper, by the way, I can prove your conjecture", or any other contact after the review process. I never had in mind whether it is ok to contact authors with questions about the paper. – user151413 Jan 03 '21 at 19:44
  • @BlueElephant See my comment right above - would this also apply to one-way correspondence after the review process, rather than requests for clarification? – user151413 Jan 03 '21 at 19:45
  • @user151413 I don't think there's anything wrong with that, but after the review is done I won't probably need to contact them. I can just prove their conjecture in my next paper and they will see it in the ArXiv. – BlueElephant Jan 03 '21 at 20:03
  • @BlueElephant True. Indeed, this was not the core of my answer, it was more a peripherial comment (I'm a bit curious whether the downvotes stem from there!). But you might feel that they might interested in knowing that, just like you might have seen their paper on the arxiv or in the journal and told them "Hi guys, I can prove your conjecture". In fact, it might also be relevant for follow-up work of theirs, so they might appreciate learning about it early. – user151413 Jan 03 '21 at 20:10
  • @user151413 Journals should primarily be interested in protecting the review process (which may involve multiple rounds) itself, so they're less likely to have policies about disclosing the reviewer's identity afterwards. Personally, I don't see much of a problem with doing that, but according to COPE's guidelines (see link above, last page) referees are expected to keep details about the review confidential post review. – Anyon Jan 03 '21 at 20:59
  • @Anyon Actually an interesting read! On the other hand, it is clearly written from the perspective of journals, not the scientific community as a whole. Following it, I'd say the majority of peer reviewers behaves unethically, given the typical time taken for the review ;) – user151413 Jan 03 '21 at 21:15