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I have two preprints to be uploaded to arXiv. In one of the papers, I cite a theorem which is proved in the other one, so the statement of the theorem is the same in both papers. Will this result in a "text overlap" comment?

Edit: What if I split up a submitted paper into two, replace the old one by the first part of the two new ones, and upload the second part separately?

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No. Source: personal experience.

The overlap thing is looking for significant amounts of overlap (many many papers will contain some overlap). I don't know what the cut-off is, but one theorem statement is below it.

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    It's probably a good idea that the exact criteria for text overlap aren't publicized - probably only the admins know fhe details. If they were, they'd be gamed.
    – innisfree
    Commented Feb 12, 2017 at 5:39

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