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Apr 19 at 17:58 history edited Greg Martin CC BY-SA 4.0
changed to inclusive pronouns—not all referees are male
Apr 18 at 22:52 vote accept mechanodroid
Apr 18 at 22:52 comment added mechanodroid @DavidWhite Thank you for your detailed answer. You have put my mind somewhat at ease. Still, only time will tell that will the outcome be.
Apr 18 at 22:44 comment added mechanodroid ... To further drive the point, they used this fact to justify rejecting the paper by making the following argument: "The proof of the paper is unnecessarily complicated. I know because I came up with a much simpler one." 5. Beyond its existence, the reviewer did not disclose anything else about this simpler proof. Neither the idea nor which supposedly new methods they were able to apply. This makes it unlikely that they would be interested in salvaging the paper in the present form. Rather, they made it obvious that the paper should be restructured entirely.
Apr 18 at 22:43 comment added mechanodroid ... This alone makes it exceedingly unlikely that a casual reader on arXiv would even skim through the paper, let alone make a serious effort to understand the proof. 3. Contrary to the previous two points, the reviewer had to go through the paper in great detail to verify the proof's correctness. As stated before, this would not be possible without a serious effort of going through many lengthy computations. 4. Most importantly (and perhaps surprisingly), the reviewer explicitly stated that after some thinking they arrived at a simpler proof using different methods.
Apr 18 at 22:43 comment added mechanodroid @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.
Apr 18 at 17:20 comment added David White @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.
Apr 18 at 17:19 comment added Dan Romik ... 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.
Apr 18 at 17:17 comment added Dan Romik 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.
Apr 18 at 12:40 comment added testaccount 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.
Apr 18 at 12:11 history answered David White CC BY-SA 4.0