I am writing a paper right now, and part of the paper makes use of a (trivial) generalization of a number of really nice theorems and constructions from a paper that was never made public. The author has left pure mathematics and has no intention of publishing the paper, but I received a copy directly from him several years ago.

The results and constructions are crucial to my paper, and since I am working with a minor generalization, I think I do need to include the proofs, especially since they aren't available. I don't want it to look like I'm taking credit for the results or plagiarizing, but some of the proofs are basically copies. I have a bunch of disclaimers at the top of the section and continually remind the reader that all of these results are in the original paper.

Do I need to not only give credit at the top of the section, but also give credit for every observation, statement, lemma, and diagram?

PS It seems like the community wiki checkbox is gone. I'd appreciate if a moderator could do that for me.

Edit: I contacted the author, and he agreed to put it on the arXiv himself. Going to leave the question up as a community wiki for anyone else who runs into this problem.

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    the most elegant and appropriate way out would be if the author of the paper you are relying on would give you permission to post their paper on arXiv (you can do that even if you are not yourself the author, with due permission); then you can just refer to it. – Carlo Beenakker Oct 11 at 20:17
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    Why a disclaimer at the beginning like "the entire content of lemmas and theorems of Section N, and their proof, is due to XYZ who was so kind to share with us his unpublished preprint" wouldn't do? – Qfwfq Oct 11 at 20:20
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    @Qfwfq That's basically what I have now, but I'm posting to get advice from the mathematical community. – Harry Gindi Oct 11 at 20:21
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    Is it particularly burdensome to write "Theorem 14 (Grothendieck [3])" instead of "Theorem 14", and "Proof (following [3])" instead of "Proof"? I sometimes wish people would do this more often, even in cases where [3] is published, so that I have a second reference in case their writing doesn't make sense to me. – darij grinberg Oct 11 at 23:05
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    Harry, take a look at section 6, beginning page 24 of alpha.math.uga.edu/~pete/Clark_Jagy_11_13_2013.pdf where Pete made a careful summary of the time line. I guess my emphasis is that Prof. Ebeling rather liked the whole business, his carefully crafted exposition having a new use. If your acquaintance feels the same way, standard (reference/credit) measures are surely enough. I'm not sure what you do if he burned all his papers in disgust. – Will Jagy Oct 11 at 23:58

First of all, if you received a paper from the author privately, and it is unpublished, you need his/her permission to use the result, and permission to mention his/her work.

When you ask the permission, you may also ask whether the author is willing to post the paper on the arXiv, and you may propose him/her to do this yourself.

If permission is granted but the rest does not work, you may include the paper in your reference list, marking it as "private communication". But this is the measure of the last resort (if the author cannot be contacted and/or gives you no permission to publish his paper).

Remark. I have some results which I consider important, and which I do not publish. The situation is exactly the same: I build on an unpublished result. The author gave me his manuscript but refuses to publish it, and does not give me permission to publish his result. Myself, I stick to the following rule: everything I use in a published paper must be available (in principle) to every reader.

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    If permission is obtained, another way out is to make a really large appendix which reproduces all of the original results and refer to that. Then it's a paper by author H, with appendix by other (ghosted by H). It is not as elegant as Carlo's solution, but it might work. Gerhard "Would It Be An Appencodectomy?" Paseman, 2018.10.11. – Gerhard Paseman Oct 12 at 0:26

Why not you approach the author and ask to join forces to write as a co-author if the other person is willing to do so? That could be a fine resolution and fair to both parties.

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    I ended up proposing this, and he accepted! – Harry Gindi Oct 13 at 4:00

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