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There is a paper that was published 15 years ago; one of the theorems in it is wrong in general. A few years ago some people told the author that this theorem is wrong as stated, but yet a partial case of it is true and is quite sufficient for the proof of the main result of the paper. Certainly, it was too late to correct the paper itself; yet its current arxiv version contains a short notice that it should be corrected.

Now, I proved a (new) corrected and extended version of the wrong result mentioned. My method of the proof has benefited significantly from the 'wrong proof'. So, what should I do (in order not to offend the authors of the paper mentioned)? I have the following ideas.

  1. Avoid citing the 'partially wrong' paper. Actually, my result is not something very much unexpected, and the proof is rather short and easy; I could have found it without reading the 'wrong' paper.

  2. Cite the printed version of the paper, and tell that the result mentioned is wrong as stated? In this situation I definitely would like to say that this result is wrong, since I will not do so nobody will understand why my correction is interesting. As is it is often the case, the wrong result looks nicer than the correct one.:)

  3. Cite the current arxiv version. The problem is that it contains a notice that a revision is necessary, but no revision is made.

  4. Ask the author(s) of the paper to put a corrected version of it to the arxiv. In this situation, is it ok to tell the authors that I do not want to cite the printed version of the paper as well as the current arxiv version?

If I choose possibilities 3 and 4, should I explain somehow (in my preprint) why I cite the arxiv version and not the printed one?

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Cite the published version and the fact that you were guided by the proof given in it. Mention briefly that the stated theorem is not correct (and, if it's easy to do, explain why or give a reference where the explanation is given). –  Deane Yang Feb 29 '12 at 9:57
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This is similar to the situation in the MathOverflow question "How Do I Fix Somone's Published Error?". A key piece of advice given there was to consult mentors or specialists familiar enough with the authors so that there was a chance for a smooth resolution. You may find other advice there useful. Gerhard "Ask Me About System Design" Paseman, 2012.02.29 –  Gerhard Paseman Feb 29 '12 at 10:33
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Deane's suggestion is right. But you should cite both the print and the arxiv version, then the read has all the info. –  Chris Godsil Feb 29 '12 at 13:27
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One general principle here is that you have an obligation to cite any source that gave you assistance, even if you are confident you could have done it without the assistance, and you should cite any source that may interest readers. (For example, it's valuable to know that the original authors acknowledged the problem in the arXiv posting.) –  Henry Cohn Feb 29 '12 at 13:58
    
Paraphrasing what Deane has already pointed out: speak the truth! I have often seen papers where people cite an older paper, celebrate it a bit, before mentioning that it had a bug or error, and then proceed to fix it ;-) Your case is more detailed than just that, but also as mentioned by Chris, it helpful to the reader to have all this proper context. –  Suvrit Feb 29 '12 at 15:24

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