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Mike
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How would you cite a result that it is not quite correct, but whose proof contains some useful ideas

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?

Mike
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  • 1