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I am writing a math paper and planning to cite 1-2 results from a non-published preprint article that I had found online a couple years ago. The original link to the document no longer works, since it was hosted on a private webpage, not published on a server such as arXiv. However, I have a PDF copy of the article and could reproduce the proofs verbatim.

For a normal journal article, I would usually just include the reference without including the proof. However, since this document has become no longer openly accessible, should I reproduce the proofs in my paper?

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    Did you try to contact the author(s) of that paper? Commented Jun 24 at 23:02
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    @MoisheKohan Yes, the email included in the note gives a bounce-back error, and I couldn't find any other contact info online. Commented Jun 24 at 23:20
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    (As a no-longer academic) it seems to me more important than normal to double-check the validity of these results... it might be that the reason the paper never made it beyond a private server is that the author, or a reviewer, found problems with it.
    – TripeHound
    Commented Jun 25 at 10:42
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    If the article you're talking about is new-ish, @TripeHound's warning about verifying it's correctness before relying on it is vey valid. Commented Jun 25 at 18:42
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    @ScottSeidman There's a slight difference in that said proofs published in the 1800's are part of the formal "academic record", and some archive somewhere likely has a copy and can vouch for its provenance, even if you would need to make an appointment and travel internationally to actually see it. (Or if the manuscript is no longer extant, there's an official record of its prior existence & contents.) This contrasts with some random personal website which never previously was included in the academic conversation, and where the only record of it is "trust me, bro, it totally used to exist".
    – R.M.
    Commented Jun 25 at 19:06

5 Answers 5

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Yes. If you claim a mathematical result, you must provide readers of your paper a means to establish the correctness of the result. If your proof relies on other people’s work, the details of that work must be accessible to your readers, and if they aren’t, you need to include them.

If I were the referee of your paper I would insist that those proof details be made available. As @JoshuaZ suggests, it would be fine to include them in an appendix in the arXiv version of your paper but not in the journal version. (But including them in the journal version may perhaps serve the readers better in some circumstances.)

Of course, you have the duty to cite the original author and give them credit for their results and proofs even if their paper is not publicly available.

You should also respect the author’s copyright. I’d be careful with quoting the proofs verbatim unless they are very short or are really lacking in any distinctive expressiveness. Also, stylistically it may be preferable to write the proofs in your own words, as that would give your paper a more coherent and consistent feel. But I don’t see the copyright issue as very important here. The needs of the scientific community you are trying to serve appear to me to be a more compelling consideration (and in one or two occasions when I had to choose between strict adherence to copyright and the needs of my community, I chose the latter).

Finally, I should add that even citing results from a preprint that is publicly available warrants some caution. Again, if I’m the referee of a paper claiming that X is true because it follows from Y, where Y is a result claimed in a preprint Y that’s not yet accepted to a peer-reviewed journal, that would give me some cause for concern. This should be judged on a case by case basis (depending on the complexity of the results claimed and their proofs, and other factors), but at the very least it’s not automatically acceptable to ask your readers to trust that everything stated in an unpublished preprint is correct, whether the preprint is available or not. There have even been situations where I cited results from a published paper, and because the proofs in that paper lacked what I considered to be sufficient detail, I felt compelled to add those details in to my own paper. (This was no easy feat, and in at least one case it also made my paper much longer and probably more difficult to get published in a good journal as a result. But I felt it was important to do, and I’m glad I did it; so are others, I believe.)

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    Plus, if the results in question are particularly useful, you'd be doing other people a real service by providing an easily accessible and citable account (to be cited in addition to the original source, of course). Dubious or missing proofs in the literature can be a real hindrance to progress. Commented Jun 26 at 11:50
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You don't have to do this, but it is not a bad idea. My suggestion would be to include rewritten proofs of what you need in your own paper, or at least the version on the arxiv, and include them there. Citing something that is not accessible anymore is essentially akin to the classic proof by citing to private communication, which is really not helpful. (Worse; sometimes the proofs sketched this way are just wrong.) Edit to add since there is apparently some confusion about this answer in the comments: you still absolutely have to cite where the proofs came from originally even when including your own rewrites of them.

Depending on the context and the journal your own work is going in, you may want to just include those proofs in an appendix which is only on the arxiv version.

Note that you cannot upload the paper itself or segments of it to the arxiv, for both copyright and intellectual honesty issues.

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    Citing is giving properly credit to people who did their work. Without proper citation, you would plagiarize.
    – usr1234567
    Commented Jun 25 at 12:41
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    @usr1234567 Citing is important for giving proper credit. But in math that's very much not the only thing it is doing. It is epistemologically that people can trace any claimed proof.
    – JoshuaZ
    Commented Jun 25 at 12:45
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    Unhelpful citation: "A proof of this is given in [inaccessible], so we don't include it." Very helpful citation: "We reproduce here the proof the proof of [inaccessible]." (Although be careful of copyright issues in the latter.)
    – Teepeemm
    Commented Jun 25 at 13:54
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    I second @usr1234567 -- I think it is a major violation of research ethics to include proofs in your paper that are rewriting material from another work without correctly attributing them to said work. Even if the work in question is obscure and no longer available.
    – a3nm
    Commented Jun 25 at 17:43
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    @a3nm It seems like there's some confusion here. No one is saying here that the original author should not be credited! I'll edit the answer to make that clear.
    – JoshuaZ
    Commented Jun 25 at 18:56
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Take care in what you include. Even though the original can't be found, someone, probably the original author, holds copyright to what you have. If you publish it verbatim it will be a copyright violation and if you don't credit it, it will also be plagiarism.

You should treat it as you would any source that you use with only limited quotations and full citation. You can paraphrase the contents with citation. You can publish independent proofs, though it is a judgement call what is "independent". You can say that such and such was proved by so and so and note any essential steps in the proof that would permit others to verify the validity.

For a citation, you can list the original link and a notation that it is unavailable. You might also check to see if it was captured by the Wayback Machine before it disappeared.

But take care. Don't violate copyright even if there is no chance of it being discovered. You need an author's permission to republish their work, even with citation.

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    I think this is a special case. It is in the public interest and fair use that such a proof be presented, as long as OP gives proper credit to the original source. I do not think it would be right to - say - let Galois' results disappear in Nirvana (even if properly credited) even if they had been formally copyrighted. It's bad enough that things like that happen to movies. The Wayback machine is of course, the best solution if it works. Commented Jun 25 at 0:21
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    Not to republish it, but restate it - I do not think it was the purpose of OP to just plain republishing it? Seriously, I cannot believe that one should knowingly throw away knowledge, just because of copyright. That would amount to legal vandalism. And Galois was an example - had they modern copyright then, would his results have to be just buried by law? This just doesn't make sense to me. I would think that restating the results and proofs falls under fair use. The library of Alexandria was burnt down 3 times, and it took millenia to rediscover some results; rediscovery is not trivial. Commented Jun 25 at 11:35
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    Yes, keyword restating (with citation, such as it may be). (Constantly thinking in terms of "scoring points by publication [sic]" is a corruptive way of thinking about making collective progress in understanding...) Commented Jun 25 at 18:06
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    @Idran "There wasn't anything lost specifically" - to add to my last point, we know of many lost works of Greek authors. They must have been in the Library. Maybe elsewhere, but there is absolutely no chance to find them, except by sheer luck (see my book recommendation). Commented Jun 25 at 23:35
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    @CaptainEmacs No, there were dozens of libraries in the same era as the Library of Alexandria; it wasn't the only one or even the first one, just the largest one and most famous one today. You're right that it must have had copies of those documents, but many other libraries that weren't burnt also likely had copies of them that were also lost just from pure time. There's essentially no original documents from that time period that survive to today because papyrus and paper simply don't last that long under normal conditions; the only ones we still have at all are copies of copies of copies.
    – Idran
    Commented Jun 26 at 14:12
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If you have a clear recollection of what was done in that non-published article, you can try to find similar work out there as alternatives.

Or you can specifically look for the works of the same author, as he could have published it under another name or on another platform. Better yet, if you know the author and have their contact information, ask for the article directly, or maybe its pre-print.

If the proofs are not too lengthy, you can try to reproduce them in your paper. Or, you could write a separate document for the proofs yourself and post it online, then reference it in your main paper.

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    For clarity, my last point means that the document online is meant as a write-up of the proofs, this helps if the proofs are just too long to include
    – Duy Văn
    Commented Jun 24 at 22:28
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    Perhaps my post was unclear, but I have a PDF copy of the document. Commented Jun 24 at 22:47
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    I don't think you can post someone else's work to arXiv, but the other options might work. Commented Jun 24 at 22:58
  • I agree that arXiv and institute's repo is basically impossible without the permission of the author, so you would need to contact the author anyway.
    – Duy Văn
    Commented Jun 24 at 23:02
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I am not sure what the issue is here. Anything can be referenced as long as you cite correctly (and, of course, don't plagiarize). For example, I have cited redacted papers in the past to highlight the error - even though such articles have subsequently become 'unavailable'. There is no privilege that prevents any work from being cited for advancing knowledge. That freedom is a fundamental tenet of what underlies the contribution to literature that academia so treasures.

In your specific example, I would cite as correctly as possible and then add a footnote that the reference is now unavailable but you acquired a copy when it was available (or words to that effect).

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    The main question is whether to include the proof in the OP's article or not. It was less about how to cite.
    – usr1234567
    Commented Jun 25 at 12:45

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