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I know that preprints deposited into a preprint server should be in a polished state. However, what should happen once it starts the review process? Should those copy-edits be updated on the preprint? What about updates when replying to reviewer's comments? What if the manuscript is rejected and I am rewriting the manuscript to be resubmitted to another journal in another format?

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In principle, anything that happens to the content of a paper before printing (ie, formal publication) should be reflected in the pre-print. So yes, if you correct a bug while the paper is in review, or revise the paper for a new submission, then you should update the preprint.

However, some journals object to authors' posting post-copy-edited (or even post-refereed) revisions. And posting a revision while a paper is under review could interfere with the reviewing process. When in doubt, ask your editor.

Frequent updates may earn you a reputation for being sloppy, especially on a system like the ArXiv that publishes the preprint's revision history. (Why didn't you fix those bugs before you uploaded the first time?) But that's still better than leaving a buggy preprint out in the wild, thereby earning you a reputation for not even knowing (or caring) that you're sloppy. The right answer, of course, is to debug your papers before you post them!

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    I agree. We should do it right the first time. However, if the author keeps improving his paper(not necessarily fixing bugs), should he revise the paper everytime or wait until he believes he finds the best way to present the paper? – scaaahu Apr 17 '12 at 8:00
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    I've clarified the question a bit more in response to your section on sloppiness. I think @Scaaahu makes an excellent point since after all, a paper isn't truly polished and best presented until it finally reaches print. – bobthejoe Apr 17 '12 at 8:28
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    I tweaked my answer. Changes to the paper's content should be reflected in the preprint. For stylistic issues, I think it's better to wait until you've found the best way to present the paper. (But to repeat myself: Shouldn't you do that before you upload the first time?) – JeffE Apr 17 '12 at 13:25
  • In general, there are more than one way to prove a theorem in a math paper. If I find a better proof, what should I do? It boils down to another question, how many revisions would be considered too many by researchers? This probably should be a separate question. I just want to avoid duplicates. Thanks to the OP for asking the question and to JeffE for answering it. – scaaahu Apr 18 '12 at 1:46
  • If you "find a better proof" more than once or twice, you probably should have thought harder instead of posting the first one. – JeffE Apr 18 '12 at 3:33

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