Are there any examples for an ArXiv publication nurturing or preventing plagiarism? First of all, this is about plagiarism in the sense of stealing ideas. Copy-and-paste plagiarism is included but not likely to happen in the cases relevant for this question.

Considering the publication of a paper prior to peer-reviewed publication on the ArXiv (or another preprint server), there are usually two main positions considering a possible theft of the idea (or somebody coming up with the same idea):


If somebody manages to publish your idea in a peer-reviewed journal before you do, you can prove that you came up with the idea first or at least independently if you have published your paper on the ArXiv. Therefore it is a good idea to publish papers on the ArXiv before they have been published in a peer-reviewed journal.
If you publish your paper on ArXiv before it is published in a peer-reviewed journal, others may steal your work and publish it peer-reviewed before you do and thus take the scientific credit. It’s difficult to attack those people since the ArXiv is not peer-reviewed. Somebody could make a living of plagiarising ArXiv papers. Therefore it is a bad idea to publish papers on the ArXiv before they have been published in a peer-reviewed journal.


Are there any example cases (or even studies) supporting either of these statements? Such examples would include, but are not limited to:


Has a peer-reviewed journal ever withdrawn a paper because it plagiarised an ArXiv paper?
Are there well-known cases of “unpunished” plagiarism of ArXiv papers? 
Has anybody ever successfully resolved a priority dispute with a publication on ArXiv?
Has anybody ever accused somebody of plagiarising an ArXiv article (with the fact that the plagiarised article was published on ArXiv affecting the outcome).


Note that it is really examples and not a theoretical analysis of the statements, I am looking for. (Neither of the two positions fully reflect my opinion and some of the soft premises¹ are debatable. However, debating about these viewpoints on a theoretical basis or attacking some of the premises is usually futile.)




¹ e.g., that scientific credit is only decided by peer-reviewed publication
If you publish your paper on ArXiv before it is published in a peer-reviewed journal, others may steal your work and publish it peer-reviewed before you do and thus take the scientific credit. It’s difficult to attack those people since the ArXiv is not peer-reviewed.


This assumes that peer-reviewed publications determine scientific credit, which may be true in some fields but isn't universal.  In mathematics, it is not relevant at all for assigning credit.  Peer-reviewed papers are of course more thoroughly checked, but they do not give you any additional intellectual credit, so this difficulty does not even arise.  (In particular, for assigning credit an arXiv paper beats a published paper with a nontrivially later submission date.)


  For example, has a peer-reviewed journal ever withdrawn a paper because it plagiarised an ArXiv paper? Or are there well-known cases of “unpunished” plagiarism of ArXiv papers?


This is a difficult question to answer, because how could you tell?  If the plagiarist doesn't copy any text, but rather just takes ideas, then it's virtually impossible to prove that anything was stolen.

In mathematics, it works like this.  If someone publicly circulates a paper, then there's a brief window in which people who have made the same discovery independently have a chance to announce this fact and claim a share of the credit.  They should do so more or less immediately upon learning about it.

By contrast, if too much time elapses, then the community doesn't count it as simultaneous discovery, but rather at best rediscovering something that was already known (which gives far less credit to the rediscoverer).  There's not a clear cut-off for the timing, but I see it as follows: days later is definitely OK, weeks later might be OK, months later is generally not OK, a year later is definitely not OK.

The biggest weakness in this system is that there's a window in which it's possible to steal someone's ideas and claim you came up with them independently.  This is certainly uncommon (indeed, claims of independent discovery are uncommon, regardless of whether they are true or false), but it's hard to know for sure how rare it is because of the difficulty of proving plagiarism of ideas.  Most claims of independent discovery are obviously true (because there's a manuscript that couldn't have been written so quickly, or there's a history of talks or discussions with other researchers, or there are nontrivial variations on the ideas and applications), but every once in a while someone makes such a claim without clear evidence.

Even when there isn't much documentation, I'm inclined to believe claims of independent discovery.  Faking this takes a lot of chutzpah and effort, it's not something you can get away with repeatedly, and it's an awkward situation you wouldn't want to put yourself in unnecessarily, so it seems reasonable to give people the benefit of the doubt.

In practice, I don't think the real danger is outright theft, where someone who wasn't working on this topic at all notices a new paper and says "That looks nice!  I think I'll steal it."  Instead, the most worrisome situation is when someone was actually working on similar ideas, but hadn't really finished sorting out the details.  When they see the paper, they immediately recognize some of their ideas, and the remaining details feel so natural that they say "Yes, that's exactly what I had in mind.  This paper is merely fleshing out my ideas."  They honestly believe that they had practically completed this work, when they might have been somewhat further than they thought.  There's a whole continuum here, from people who are basically right in their beliefs to those who are completely wrong, and it's not clear where to draw the line.

Of course I have no idea how often someone claims independent discovery based on exaggerated beliefs (again it's basically unprovable), but I imagine it happens occasionally.  It's certainly unfortunate if it takes place, but it's not nearly as bad as outright theft.  The worst-case scenario is having to share credit with someone who is less deserving.