Coauthor wrote a small part of the paper then ghosted us

Question

Me and my coauthor are writing a (math) paper with a third person who initially has been very active, mainly in the form of conversations and planning, and then after writing some parts, disappearead and proceeded to ignore every attempt to get in touch with them.

Let me note we are aware they've been in contact with other people we know (and active on social media). So, as far as we understand, they simply chose to ignore us. Everything was running smoothly and we didn't have a fight or a discussion so we are very confused (and annoyed) by this behaviour. But anyway, we carried on writing our paper.

Now we are very close to submission (on arXiv, for the moment) and we are pondering what to make of the third author's name. We thought of removing their name from the authors list since their behaviour has been quite unacceptable. We ended up doing the great share of the work ourselves, and there hasn't been any reasonable motivation from their part on why this is so. On the other hand, they provided valuable input and even wrote up some parts which, even after some revisions, will end up in the paper, making up, say, 5-10% of the content. These are things they wrote before disappearing. So it seems correct to attribute authorship where due.

On a more pedantic note, they don't know the state of the paper we are going to submit so, as far as we know, we might not have their permission to put their name on it. We are going to ask them but, at this point, it's unlikely they are going to reply.

Hence, what shall we do? Is there a middle ground like mentioning their contribution in the 'acknowledgments', perhaps indicating they have been closely involved in the writing of some parts?

EDIT: after some pondering, we changed the paper to remove the small written contributions (which were proofs) made by the ghosting coauthor and replaced with alternative proofs (using a completely different approach) written by us or referenced from literature. We plan to still acknowledge them in our paper, for the parts they've been involved to, but not to have it in the coauthors list anymore.

Answer 1

Hence, what shall we do? Is there a middle ground like mentioning their contribution in the 'acknowledgments', perhaps indicating they have been closely involved in the writing of some parts?

You are including content that can be directly sourced to someone other than you to substantiate arguments put forward in your article. You have bound them as co-authors by this action. That they wrote something and then disappeared does not change this fact. That you may have made modifications to their source content before adding it to the final document does significantly not change this fact. That the relative amount of the contributed content is by some measure quantifiably small does not change this fact.

The possible choices are demonstrated as below.

• Remove all content from the other person. Remove and/or revise all ancillary content that leads to or derives from that removed content. Make the article self-contained such that it demonstrates only what you and your other co-author have written. Make the contribution from the other person only relevant for how it guided your work rather than relevant in its own right because it supports the assertions being presented. Submit the article with just you and your other co-author. State an appreciation for helpful discussions from the other third party in the acknowledgments. Send the submission to the other person by email.

• Do not change the article. Put the other person on the article only in the acknowledgments. Send a hard copy of the article by return-receipt registered mail. Include a cover letter asking for confirmation within a respectable time before the article is submitted. State that a lack of reply will be taken as acceptance to the article as written. Be prepared to learn that the other person insists on co-authorship.

• Keep the other person on as coauthor. Send a hard copy of the article by return-receipt registered mail. Include a cover letter asking for confirmation within a respectable time before the article is submitted. Be prepared that the other person must also concur electronically as a coauthor at the time the article is submitted.

These are drawn somewhat to legal or official courses of action. Independently, from professional standards, you will want to reference your discussions with the other person at the start and throughout the project. The hard question to answer is this: Were any statements made by you or your other co-author, verbal or otherwise, at any point during the collaboration that in any way promised or even implied co-authorship in return for having contributions to the project? If the answer here is not a resounding no, you may appreciate that the respectable, professional approach is to accept the other person as co-author even with the reservations you have. Lesson learned. Next time, be clearer at the outset on how you anticipate the rewards to the project (a published journal article) will be divided.

Answer 2

You cannot list them as a coauthor without their concurrence. Include a substantial acknowledgement of the contribution - perhaps with explicit credit for the proof of Theorem X.

Send them the draft. Tell him politely that you plan to post this to arXiv and ask for any corrections. You could say that if you don't hear back you'll assume what you've written is OK.

If they reply that they would like coauthorship then I think you should do that, even if they do not resume work on the ms.

Answer 3

5-10% of the content of the written paper does not mean 5-10% of the intellectual contribution. Conceptualization, design, and planning are often the most important parts of a project. Although being uncommunicative is unusual (although not unheard of), senior scholars in my field often help conceptualize and design and project, and leave it up the juniors to manage data collection and analysis, and write.

To me dropping them from the paper or posting the paper without their consent are both very bad professional behavior---at least as bad as them going AWOL, if not worse. Their bad behavior is private, between colleagues, you would conducting a public misstep on the academic record. I think you need to push harder to contact them. Call them, write again with "IMPORTANT, TIME SENSITIVE" in subject line, ask a colleagues of theirs you know to check in. I would not proceed without a response from them and, importantly, I would not work with them again in the future. But for this project, they are a co-author until they tell you they want out.