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In reviewing a paper I notice that the result presented there can be improved. However, the improvement may not be significant enough to appear in a good journal. Therefore, to me the best situation would be to have the authors' permission and to join the paper under review.

I would like to be advised of what I may do. I think I may write to the editor, and I would especially like to know how to ask politely. Would anyone have similar experience?

Edit: First of all thanks a lot for all suggestions! I just forgot to mention that my report was already sent one month ago. Would there be something extra I should take care of?

Edit 2: Again, many thanks to you guys! Actually contacting the authors is never an option in my mind. My options are only: (i) tell the editor (not recommending myself as a coauthor); (ii) write my own note. Here note means a short paper, since my new short proof may be of ten lines (the original proof is three pages), that's the reason I would like to consult you guys, and to see if there is a third option. At the moment, I prefer to do the first option, and I am thinking of whether in the email to editor I should include my new proof, or just say "I may further provide the details". How do you guys think?

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    Especially with anonymous peer review, "muscling your way in" to an authorship would seem very unusual to me, especially since from your position as a reviewer you have some leverage over the authors. It might be better to just suggest the improvement in your review, and leave it up to the authors whether they want to act on it. – ObscureOwl Jan 14 at 12:51
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    @ObscureOwl That's true, and that's why I hesitate. – Salomo Jan 14 at 12:53
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    Highly related: academia.stackexchange.com/questions/160761/… – Snijderfrey Jan 14 at 13:54
  • Worth asking yourself how you would view it if an anonymous reviewer requested co-authorship of one of your papers and would only disclose some helpful contribution if you agreed? I suspect most would be rather happier if the reviewer simply passed on a helpful suggestion that improved the paper. In my career I have greatly benefited from helpful reviewers (including directions for improved proofs), so I try to be helpful when I can to "pay it forward". – Dikran Marsupial Jan 16 at 17:39
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Contacting the authors directly is a terrible idea. Don't go there. Contacting the editor with a question or request is fine. If you contact the authors directly and they interpret it as a form of poaching and complain to the editor, you may lose the opportunity to review in the future.

But the "best" option isn't to join the paper. It is to give your best review, pointing out what you think has been missed and asking for major revisions if that is what it would take.

Tell the editor that you would be willing to work with them on the improvement with permission and await what happens. You may not get a co-authorship (I doubt you will) and your advice might even be attributed to the anonymous reviewer, but that is pretty natural.

You will have contributed to the advancement of the art.

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    +1 It's very bad form to do so and nearing academic misconduct, as a reviewer wields an inordinate amount of power. @ObscureOwl has called it "muscling your way in" and I couldn't put it better myself. – Captain Emacs Jan 14 at 14:37
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Q: When I spot a possible improvement while reviewing, can I suggest to join the paper as a co-author?

NO. This would be unethical and unprofessional. Buffy's answer provides guidance for your best course of action: go through the editor and suggest improvements.

However, a comment made by the OP motivated me to provide an additional answer on why this is bad idea:

Thanks GEdgar! My field is math as well, the paper is written by 2 authors. I should confess that I really need publication, and I am really afraid if I were put in the acknowledgment after sharing. Therefore I am struggling whether I should write to the editor or just write a note by myself. Would you have any suggestion?

Contacting the authors to be added because you really need publication is a horrible idea because

  1. You would be violating the blind system of review most journals use.
  2. As a reviewer, you are in a position of power (albeit not much power) and your suggestion or request for addition as a co-author would not be one as a peer. However, another answer noted situations where the poster has been invited to be a co-author after suggesting ideas. But, in that case the the reviewer suggested ideas and other people though the reviewer should be a co-author.
  3. If you do this, you may soon find yourself with a bad reputation in your subfield.
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It sounds like you're approaching the review process from the wrong angle and are looking for ways to contribute to the results of a paper.

Remember that every single paper ever published could have been better! Your main job as a reviewer is to judge the merits of the paper as is. Additionally, you should/can make suggestions as to how the paper could be improved. But these are expected to be helpful suggestions around the edges that would not warrant authorship. Unless the situation is extremely unusual, it is inappropriate for you to suggest new experiments that you could perform or new results that you could derive and subsequently suggest yourself as a co-author.

This is a social norm in science for which there are several reasons. Yes, there are some aspects in which science could be improved by following a different norm (e.g. this post can be improved by someone else who will become a co-autor!), but this is the currently accepted norm.

(Truly exceptional circumstances in which this norm can be violated is if you have the missing piece in an urgent and important problem that would change the field if included in the paper. Say, the whole paper is about an extremely important conjecture and you happen to have thought of a proof of it during your review. Or you have the missing experimental evidence that is the key to show that this drug is not just a reasonably good candidate to work against SARS-CoV-2 but in fact almost proven to work! Then you may contact the editor (but not the authors) with your suggestion. Simply having an idea for an incremental improvement is not enough to offset this strong social norm.)

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In my opinion if the improvement won't be significant as stand-alone work you should disclose it to the authors within your review.

If it is a real substantial improvement you can recommend - from your referee point of view - that it must be included. You will likely be acknowledged (anonymousy, of course). I do not think acceptance is under discussion anymore independent of the fact that the authors comply or not.

Conversely, if you have something publishable at hands, wait a bit then go on your own.

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What field is this? Would the paper go from 10 authors to 11? Or would it be 1 to 2?

My experience is in mathematics, where papers often have 1 author. I have seen in such papers something like: Thanks to an anonymous referee for the following proof.

Another case involving me. A paper by 3 statisticians, acknowledging me for providing a proof. The journal asked them to add me as author, so in the published paper I am one of 4 authors.

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  • Thanks GEdgar! My field is math as well, the paper is written by 2 authors. I should confess that I really need publication, and I am really afraid if I were put in the acknowledgment after sharing. Therefore I am struggling whether I should write to the editor or just write a note by myself. Would you have any suggestion? – Salomo Jan 14 at 12:50
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    @Salomo Don't do it. If you need a publication, write your own. The cases where I have seen such things done are considered outright misconduct; in one case, the perpetrator was a very powerful academic, so nobody touched them; but in principle they should have. In an other case, the perpetrator was effectively ostracized. Don't ride on others work. If they are graciously giving you coauthorship, that's fine. – Captain Emacs Jan 14 at 14:41
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As you describe the situation all you should do is to mention in your report that Theorem X can be improved to obtain Theorem X'.

But one can imagine other scenarios. One of the celebrated mathematics papers of the last century, published by two authors H & H', originated - according to H' - as follows. Author H' submitted a paper; it was sent to referee H who had in his filing cabinet an unpublished manuscript overlapping by about half the material; the editors intervened, the paper was withdrawn, and finally H & H' published a paper developing and expanding the union of the drafts.

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I assume here that by improvement you meant something like a way to prove a more general case of a theorem presented or a suggestion for a corollary.

As a referee your job is to judge the quality of the paper as it is presented to you. You are not expected to suggest additions or improvements to the results presented in the paper. After all, all research is incomplete by its very nature.

So what are your options?

I would definitely not contact the author(s) directly. This is a breach of an implied agreement of secrecy between you and the editor. Most journals explicitly require that all communication should go through the editorial office.

I would also not propose myself as a coauthor if I was in your situation. There are a few reasons for that:

  1. There is arguably some randomness involved in you getting the draft for review, so it is a bit unfair.
  2. You put the editor in a tough position of having to mediate a request of coauthorship between you and the author(s) of the paper.
  3. It is, after all, their paper with their ideas and execution. If, by your own admission, the result that you want to add is not worth a standalone publication, perhaps is unfair that you share an equal amount of credit by cosigning the paper with them.
  4. If the author(s) refuse to include you then the situation would become exceptionally unpleasant because now they know your unpublished idea and you run the risk of getting scooped.

One way is to propose the addition in the report and accept to be thanked as an anonymous referee. However, keep in mind you cannot ethically reject the paper if they refuse to do it because you are not asking them to fix something but rather to add something.

If you are happy with being acknowledged, but you would like to be acknowledged by name, you can give the editor permission to disclose your name to the author(s). Then the editor will decide whether it's ok or not.

The final option is to type the theorem yourself (citing that paper) and to find a less prestigious journal on which you can publish. I understand that publishing as a preprint-only is not an option for you at the moment, but in principle one might also do that.

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