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My project was based on a famous paper, which, unfortunately, contains a major mistake, discovered by me. Since I already spent a huge amount of time on this direction, I submitted my "correction result" and presented it as a new paper. I made this decision due my advisor's advices and this site.

However, the editors just made a decision that my paper is only publishable if I rewrite it as a concise corrigendum with less than 1500 words.

While I have no problem in serving the community by writing a corrigendum, I am a bit confused, because:

  1. For a correction note, the authors are usually the original team (but not always).
  2. For publication of comment or correction note made by others, the original authors are usually contacted by the note authors first (I have not done this).

Does the current situation sound normal?

High GPA
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    Is this a math paper? If so, did you correct a proof or show that a theorem there is false? Or what? For some things a new paper is appropriate for others, just a correction. – Buffy Jun 14 '22 at 13:16
  • I showed that a theorem (and its proof) is false and provide a corrected version – High GPA Jun 14 '22 at 13:48
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    Do you have a counterexample to the original theorem? – Buffy Jun 14 '22 at 13:53
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    This sort of practical question that depends heavily on specifics is something you're going to need to talk to your advisor about, not strangers on the internet. – Noah Snyder Jun 14 '22 at 14:41
  • @Buffy I do have a counterexample. – High GPA Jun 14 '22 at 15:01
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    @HighGPA Do I understand correctly that the original author was your previous advisor, and you haven't yet informed them of your results at all? Unless they are deceased, unreachable, or you are no longer on speaking terms with them -- the usual advice would be to contact them first. – academic Jun 14 '22 at 16:58
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    @academic That was another paper. I do not personally know the original authors. – High GPA Jun 14 '22 at 17:35
  • "the original authors are usually contacted by the note authors first (I have not done this)" Why haven't you contacted the original authors? It seems that this would have been the canonical thing to do (actually, before submitting your counterexample and corrected result to a journal). – Jochen Glueck Jun 14 '22 at 18:35
  • @JochenGlueck For correction paper yes you are right it is canonical thing to contact the original authors first. However, I presented the results in a new paper, and my advisor suggested a direct submission rather than contacting the original authors first. – High GPA Jun 14 '22 at 18:57
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    @HighGPA: What I don't really understand in your comment is the word "rather": it is possible to contact the original authors, hear their part of the story, and then still submit your findings as your own paper. Frankly, if I learned that somebody found a serious mistake in one of my papers, published a counterexample and a corrected version of the result, and did not even bother to tell me about it, then I would be... let's say, not amused. – Jochen Glueck Jun 14 '22 at 19:03
  • @JochenGlueck I get your feeling. I should've think twice. My advisor just taught me how to organize the paper and told me to directly submit the paper to his suggested journal; he did not suggest me to (or not to) contact the original author. – High GPA Jun 14 '22 at 19:13
  • @JochenGlueck Hi Jochen, I understand that you are not amused if I find a mistake in your paper and does not tell you. In a related case, if I write a paper heavily based on your previous papers, will you be not amused if I did not contact you before submission? – High GPA Jun 28 '22 at 00:42
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    @HighGPA: I'd say this is a very different situation. If somebody builds heavily on my work I'll simply be happy when I find this out. It would be a nice courtesy if they also tell me about (no matter whether before or after submission), but I would not bother if they don't. – Jochen Glueck Jun 28 '22 at 08:51
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    Can you update us? how did you solve this pressing issue? – EarlGrey Jun 28 '23 at 12:03
  • @EarlGrey You are right sir I forgot about my post here. I decided to contact the author. The update is here https://academia.stackexchange.com/questions/197600/ – High GPA Jun 28 '23 at 12:31

3 Answers3

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If you have a proof that the original paper has a serious flaw, such as using a counterexample to show that a stated theorem is actually false, and you also provide a correct theorem and its (correct) proof, then this feels to me like it is sufficient for a new paper, not just a correction. This seems (to me) to be especially true for an important paper. I'm not the one judging, of course, but it seems like grounds for a discussion with the editor.

Moreover, since you make an intellectual contribution to the field, you should get authorship status on whatever is published. The "normal" action may not be appropriate.

Another option is to withdraw the work from this publisher and submit it elsewhere. If your new proof is novel in some way, then I think you have both an argument to present to the current journal and grounds for publication elsewhere.

But, as with most things, novelty is an important consideration and the editors/reviewers may have decided that what you have lacks that element.

Buffy
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Without knowing the details and reading your paper, it is hard to tell. In any case, it is your paper with you as the author, even if it is called a correction.

Mathematics editors are notorious in asking for shorter versions. You need to decide whether you can comply with the editor's limit or not. If the theorem is famous, you will have made your mark. You should feel free to submit to another journal. You can also use the 1500 words to prove the theorem wrong and then publish elsewhere your version of the theorem.

Thomas Schwarz
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Contact the original authors

Unless you have very good reasons for not doing so, I'd urge you to contact the original authors of the mistaken paper. If your work gets published then they will hear of it -- better that they hear of it from you first!

Assuming your work is correct, they are likely (if not certain) to be gracious. They might give you useful advice, or even publicize your work for you. (Here is an example of a mathematician calling attention to an error in their own paper, with credit to the person who found it.)

If it happens that your own work is incorrect, then they are likely to catch and point out the mistake.

Depending on the circumstances, the result might become known as the Them-You theorem, which would very likely be good for your career. Here is a prominent example, where the correction paper was published in the Annals of Mathematics! So don't sell your work short, and consider submitting to a different journal, especially if you contact the original authors and they are encouraging.

academic
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