Unable to decide if I wait for my coauthor for indefinite time? Not sure even if my coauthor deserves authorship

Question

I am PhD student in mathematics, from Aisa region. I started a project in 2020 and a (assistant) professor from Europe formally promised to work together. This is my old question here, here, and here. I am going to be details here (sorry), so that, readers can understand the situation:

My coauthor(?) didn't cooperate with the results of the paper. Every time, after partial progress from my side, I used to send those results to him through emails, seeking his help to shift my results for further improvements. But he was irregular in communication; after a couple of emails in 2-3 months, he used to reply once with the promise that he would look into it. But ultimately, nothing happened. This procedure continued until 2022. I was very upset due to this. Finally, I completed the whole paper (with the help of other professors) at the beginning of 2022 and again sent the final paper to him to look into and revise the paper in a nice way because my language writing is not that creative. I suffered in publishing my previous article due to poor writing. My whole intention from my coauthor was that he will read the paper, check the calculations and revise it in a creative way before submitting it to journals. So far he did nothing but this time he read the paper and point out a minor error in two results, but then I have then corrected those errors on my own. So I am grateful to him for pointing out two errors in my papers. After correcting two errors, I sent the final revised version to her in March 2022 and asked him to revise the language and submit it in a journal, but since then he has continued to promise to revise and submit the paper. Indeed, I was happy to offer him authorship, though I am not sure if he really deserves to be an author(?). But 2022 passed, 2023 is almost finished, and still he is not taking action. After failing to communicate at several attempts, I said that if he doesn't finish the paper by September 2023, I will have to submit it in arxiv because I wanted to mention the paper in the few post-doctoral positions as my proposed research plan will be based on this particular paper, and that is why I repeatedly requested that he submit the paper in arxiv at least so that I can show the paper in my resume. But he still didn't reply within September, and hence I submitted the paper in arxiv (without his name since I got no consent from him) and acknowledged him. I sent him an email and mentioned that I have submitted the paper in Arxiv but will not submit it to a journal. As soon as he revises it, I will update the paper in Arxiv and add his name. This time he replied and said to add his name to the paper "as soon as possible," with some strong words. and he said he has been unwell since September 2023, so he couldn't reply. In my response, I stated that I had submitted the version to arxiv, for which I was solely responsible for all of the results. He knows it that he didn't do anything and that is why in his next reply he became soft. I then requested that he revise the paper and submit it to the journal. Since it is a health issue, I am emotionally more in favour of him and truly want him as a coauthor. Besides that, he is an established mathematician, so it would be slightly beneficial if he remained as a coauthor. But I can't understand if he has really been in the hospital since September 2023, though he is replying to emails regularly (since I submitted the paper in arxiv). This is something that I am stuck at. Suddenly, I saw in his profile that he mentioned the paper title in his CV and mentioned it as a preprint (preparation/submission). Of course, he mentioned me as an author as well. This is why I don't want to upshet him by proceeding alone. So here is my question:

• How long should I wait for him, or should I proceed as a solo author?

• Does he really deserve a coauthor (for pointing out errors)?

• Is he just holding onto the project but not interested in it?

I appreciate your valuable suggestions that I really need. I am suffering the situation for long time. Even if I exclude tese 3 months of his unwell, in the last one and half years, he did nothing significant as coauthor. I am a PhD student and suffering this bad situation.

Answer 1

This is a tricky situation. I think what you do depends on whether or not he ever met the criteria for authorship in the first place (not necessarily if he continues to be actively involved). I can only offer the perspective from my field, which is not mathematics, but there are specific criteria that I follow for authorship.

Generally, one must make a substantial intellectual contribution to the paper. They must then also take part in the writing/revision process. Then they must approve the publication and agree to be held accountable for the results. Meet all 4 points and ethically they must be listed as an author (unless they decline I suppose). In your case, I don't see clear evidence that any of these were met, even in the beginning. You know your situation better than I, though.

So if you decide that he did not in fact contribute significantly, I would say you don't really need to include them as an author. It would certainly burn a bridge, but it sounds like the relationship may already be soured anyway. The only caveat here is that if they did initially contribute significantly, you must give them the chance to meet the other criteria. The way ICMJE words it is:

The criteria are not intended for use as a means to disqualify colleagues from authorship who otherwise meet authorship criteria by denying them the opportunity to meet criterion #s 2 or 3.

So the rub comes from the fact that while you have offered them that opportunity and they have not done anything, they clearly want to be listed as an author. I think your options are to either list them as an author and move on or firmly state you don't feel they meet reasonable criteria for authorship.

Obviously these exact rules may not apply directly to mathematics, but I think they work as general guidelines for most fields.

To answer you questions directly,

1. There is no time limit on authorship. They either contributed enough to warrant authorship or they didn't. They can't just time out, especially since they are responding and indicating they want to be included.
2. This is the crucial question. Based on my experience and what I'm reading here, no. I often ask colleagues/mentors to review my papers. Unless they make significant additional contributions I don't include them as authors. I have offered authorship in the past, but with the understanding that moving forward they would contribute to the level of an author. This strategy might not hold true for mathematics though. It probably also depends on how significant the errors where - I assume a fundamental error is different than typo's or minor mistakes.
3. I can't answer this. I don't know why he would be "holding on" but have no interest in publishing. I suppose it's possible that he is trying to scoop you but that seems unlikely given the series of events.

I do wonder, you collaborator seem okay with the preprint (as long as they are listed as an author). Why not just submit the paper yourself and list them. It isn't ideal but you could move on from this project. Just don't collaborate with this person again. There are english language editing services available if that is a concern to you. I think whatever you do, you should talk to the other professors who helped you. They may have some insight that I do not.

Side note: I sympathize with him dealing with an illness, but that doesn't really change his contributions thus far. Personally, I may give him a little extra leeway as a result, but at some point, enough is enough.