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I had a research article posted in arXiv on November 2020 and it is currently in review by a leading journal, I call it J1. Today when I was browsing research papers, I found that a research paper has been published in a lower tier journal (let's call it J2) and it has one section with ideas that are very similar to mine. The paper published in J2 was sent for review on 1st Feb 2021 and it got accepted on 15th Aug, 2021 (per the dates given on the website of the journal).

The section which is similar to mine has results which form the main idea of the paper and I find that it has been allegedly stolen. I am amazed how my paper which is already on arXiv can get scooped like this. Obviously the wording has been changed by the authors but the main idea in the section is the same as mine.

I am confused what should I do now. How do I prove the plagiarism, whom should I reach, and how should I approach this? Is the fact that their results in Sec 1 are similar to mine and I have published it first on arXiV not a valid claim to prove that my work has been scooped?

I am in my PhD days and the author who has done this is an Assistant Professor.

Note: By "similar" I mean that the results obtained in Section 1 of the paper in J2 and the results obtained in my paper in J1 are the same. The other sections of the paper i.e. Sections 2 and 3 in J2 are different from mine. But the results in Sec. 1 are very important and form a base for the other sections of the both the papers in J1 and J2.

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    Are you sure the other authors did not come up with the same idea independently? Do you have any specific reason to believe they stole it from your paper?
    – GoodDeeds
    Sep 29 at 14:26
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    Sure, but in that scenario "stolen" is too strong, it suggests malicious intent. That's one possibility, the other is that they simply did not know of the existence of your paper (especially given how many papers get put on arXiv these days). I am not sure what you should do (since the other paper is already published), hopefully someone will provide a good answer.
    – GoodDeeds
    Sep 29 at 14:33
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    @Math_Freak Many similar ideas pop up at the same time. The are - so to say - in the air. E.g. calculus, for a famous example. Heisenberg and Schroedinger, for another one (although equivalence was not obvious at the beginning). So, unless you can really make the point that they really copied nonobvious statements from you, you should be careful with the word "stolen". As for studying previous work, yes that should be done. But there are so many publications that it is impossible to be sure one covered everything. Many ideas get forgotten and rediscovered multiple times, in all honesty. Sep 29 at 15:01
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    "Why the downvotes?" I did not downvote, but in my opinion the problem with this post is that you did not show anything that would suggest that the authors of that paper were even aware of your work, yet you catergorically claim that they stole your idea. If you truly believe that they knew about your work, you should explain why. "the main idea in the section is the same as mine" is simply not convincing—it could be entirely accidental. If there is anything else, mention it.
    – Szabolcs
    Sep 29 at 15:16
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    Expanding on @Ian's comment, it is quite possible that not only did the authors of this paper not read your arXiv submission, but the reviewers didn't, either, otherwise they likely would have recognized the similarity and suggested to the authors that they cite your preprint.
    – Bryan Krause
    Sep 29 at 18:08
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Simultaneous discovery of research ideas is an entirely normal occurrence in academic research. It happened to me several times over my career so far, and I’m just one guy — some versions of this happen to practically everyone who works in crowded, competitive research areas.

I am confused what should I do now.

What should you do? First of all, take a deep breath and think very carefully about the seriousness of your accusations and whether they are substantiated by hard evidence. You have at least one very clear misconception in your post and follow-up comments, namely the belief that other people must know about your work if they are working in the same area, because it is posted on arXiv. That’s absolutely not true. How would you feel if someone accused you of misconduct because you failed to cite a relevant paper of which you were unaware? Have you read all the literature in your field? I bet you wouldn’t feel that that was a very fair accusation if someone accused you of stealing someone’s work that you never even heard about.

After taking a deep breath, my suggestion is that you show both your paper and the other one to an adviser or senior colleague, and ask for their advice on how to proceed. Quite possibly there isn’t anything you need to do — mathematics journals are quite tolerant of publishing independent discoveries, and in any case your posting to arXiv will establish precedence in the unlikely event that people care enough about this to make an issue of who has priority over the ideas. You may want to contact the authors of the other paper and point them, diplomatically and without any hint of accusation of wrongdoing, to your own work. And you may even want to cite their paper or add a discussion to your paper of how their ideas relate to yours — that depends a bit too much on the details so I don’t feel I can advise you precisely. Regardless, please don’t accuse people of stealing ideas based on such flimsy evidence. That is a very serious matter and could badly hurt your reputation.

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  • Shameless plug: do the same, you would do, if you were "just" interested in that other paper. Oct 1 at 18:18
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So far, nothing in your question at all indicates they have indeed stolen your results. You can claim you came up with them earlier, but the history of science has had plenty of occasions where the same results were formulated independently with years, sometimes even decades or centuries (!) separating them. This seems the most likely conclusion.

In general though, if you have a more reasonable suspicion (similar or identical wording, order of points they make, similar-looking data, sometimes even stolen figures), that is an ethical issue to be raised with the editorial board of J2. Make sure to have proofs, and these proofs should be as rigid as the proofs in the articles you're writing.

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It could be that the paper in J2 first appeared as a preprint much earlier than Feb 1, 2021. It could be also that it was first submitted to another journal and was rejected there. So before you make any accusations, you should contact the authors of the paper published in J2.

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    Actually you should contact them for lots of reasons. But don't contact them with an accusation.
    – Buffy
    Sep 29 at 16:15
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Your arXiv preprint shows that you had the idea first. Does the subsequent paper in J2 harm you in any way? You can still demonstrably claim credit for your work in subsequent papers, job applications, etc.

Finding whether there was plagiarism or not, in addition to being difficult, would not be useful to you. It might be useful to your competitors' employers and more generally to the community, but this is probably someone else's business.

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