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I am wondering what is the etiquette of publishing a "folklore" result?

Though special cases of the result are well-known, the proof is not readily available in any reference text or paper I've seen. I will include it in the background of my thesis, and I could stick it onto another paper which I am working on (in which I use the folklore result). However, the paper I am working on is in a very niche area, whereas the proof of this result is useful to the bulk of researchers in my field.

My options are:

  • Include it in my current paper, which is in a niche subfield

  • Put the result into a (very) short paper and submit it to some journal

  • Post the proof on arXiv, and not submit it to a journal

  • Post the theorem and proof on nLab

What are your thoughts? Are there any journals that accept this sort of "folklore" publication? Or am I better off just sticking the proof in my current paper or posting the proof on arXiv or nLab?

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    $\begingroup$ I think at the very minimum write it up, if it can be (relatively) self-contained and pop it on the arXiv, labelling it clearly as folklore. You might as well get magic beans for the counters to count for your efforts, if they are nice enough to count the arXiv as a real bean. If you make the paper expository, it might end up in a journal that caters for that type of article. $\endgroup$
    – David Roberts ♦
    Mar 9, 2017 at 6:50
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    $\begingroup$ See eg mathoverflow.net/questions/15366/…, and see Pete Clark's answer academia.stackexchange.com/a/38109/8881 discussing how he approaches the matter. $\endgroup$
    – David Roberts ♦
    Mar 9, 2017 at 7:38
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    $\begingroup$ Dear ಠ_ಠ, out of curiosity, what is the result? (I am hopeful it pertains to SDG) $\endgroup$
    – Arrow
    May 29, 2019 at 9:59
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    $\begingroup$ I do not want to bump this old question with a new answer, but I wanted to point out that the story of one folklore theorem is told here: oliviacaramello.com/Unification/… The author asserts that the community was biased against her. She created this controversy and got senior people to admit that, while her result was folklore, it hadn't been published before. She's now a full professor. But, in general, I advise against this kind of conflict with senior people in the field. $\endgroup$
    – David White
    Jan 13 at 16:09

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You ask for the "etiquette", which may differ from field to field. For the research community in computer science, the fate of one particular folk theorem has been documented in loving detail by David Harel in On Folk Theorems (1980).

One thing to note from this exposition, is that a characteristic of many folk theorems is that they are vague ("While-programs compute everything" is the particular example discussed by Harel), so they give rise to more than one version, and each version requires a seemingly different proof. Harel finds over 50 references to proofs of various incarnations of this folk theorem:

These proofs, which span fourty-four years, also span the complete spectrum of recognized scientific literature: textbooks, monographs, survey articles, journal papers, conference proceedings, newsletters, theses, technical reports, lecture notes, letters to editors, and self-referential folk tales.

So I would conclude that for this field at least, publishing a proof of a folk theorem in whatever medium you find most convenient is "proper etiquette".

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    $\begingroup$ But once a proof is published, it's no longer a "folk theorem", right? $\endgroup$
    – Gerry Myerson
    Mar 9, 2017 at 10:39
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    $\begingroup$ @GerryMyerson --- that's the point made by David Hared: a folk theorem needs a certain vagueness: The vagueness in a theorem's statement gives rise to more than one version of it, and it becomes more fun and more folkish when each version requires a seemingly different proof. $\endgroup$
    – Carlo Beenakker
    Mar 9, 2017 at 10:53
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Include it in your paper, and write clearly that on your opinion this is a known result but you could not find a reference. You can never be sure that this result has not been published by someone, and you just don't know.

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    $\begingroup$ I have a published paper which I'm pretty sure has never been read except for the part that explains a piece of folklore. $\endgroup$
    – Alexander Woo
    Mar 10, 2017 at 6:21
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    $\begingroup$ @Alexander Woo: this frequently happens, and not only with "folklore" but with the well-referenced 19 century of early 20 century results. People are lazy to read old papers using old fashioned notation. $\endgroup$
    – Alexandre Eremenko
    Jun 17, 2020 at 16:42
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Or, you can do as they (Phelps et al) did at U Washington, and publish numerous results under a pseudonym (Rainwater in this case) ....

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    $\begingroup$ The arXiv seems not to take submissions from J.R. these days ... :-( $\endgroup$
    – Yemon Choi
    Mar 14, 2017 at 18:01
  • $\begingroup$ Moreover, I think that since journals are keen these days to avoid "fraudulent" papers, the conditions of submission are such that one would have to create an email address etc on J.R.'s behalf if one tried to submit under his name. $\endgroup$
    – Yemon Choi
    Mar 14, 2017 at 18:03

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