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This is the correct answer, and good advice. In pure math, I believe in general people are pretty careful about attributing results, at least recent ones. You can find many papers with notes such as "Theorem 1.1 was also obtained independently by X and Y in ..." when two groups prove similar results around the same time.
– testaccount
Commented Apr 18 at 12:40
2

I think most of this answer talks about a scenario that is quite different from what OP asks about. OP wrote: "Their paper could even acknowledge that the original researcher made them aware of the result", indicating that they are not thinking of a situation in which the reviewer makes active efforts to pass off the theorems in the paper as their own; rather, the reviewer cites the earlier work and publishes a paper claiming only the novel element of "shorter, more presentable proofs". That situation is the one I address in my answer.
– Dan Romik
Commented Apr 18 at 17:17
... As for the situation of a reviewer committing plagiarism, that would indeed be very unethical. However, to the extent that this is something OP needs to worry about, I don't see why they need to be more worried about the reviewer committing this plagiarism than about anyone else committing it. As I said in my answer, once the paper is on arXiv literally anyone can try to improve on it (and literally anyone can plagiarize it if they wish to behave unethically). The reviewer has no special advantage, and no more incentive than anyone else does to behave unethically.
– Dan Romik
Commented Apr 18 at 17:19
@DanRomik I addressed that part of the question ("Their paper could even acknowledge...") in the middle of my answer. But, because the OP was asking whether uploading to arXiv could protect against the scenario, in the beginning of my answer I was assuming the paper had not been uploaded to arXiv and was not publicly available. From the mid-point of the answer on, I address how putting the paper on arXiv changes things. I think most of what's in your answer is already in mine, but, hey, it doesn't hurt for the OP to hear it twice.
– David White
Commented Apr 18 at 17:20
@DanRomik "...why they need to be more worried about the reviewer committing this plagiarism than about anyone else committing it." The paper is indeed already on arXiv but I have several quite specific reasons to be worried about the reviewer in particular, rather than anyone else: 1. The result is quite obscure and unlikely to attract the attention of the right people who would be even interested in shortening the proof. 2. The paper is indeed quite long, technical and contains lengthy computations which are themselves very elementary but extremely tedious and difficult to follow.
– mechanodroid
Commented Apr 18 at 22:43

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