TL; DR; Where can I publish proofs that are not groundbreaking nor profound?

I recently found an integer sequence in the OEIS. Okay, the OEIS only contains integer sequences, so nothing new so far. However, the entry for this sequence mentioned an upper bound that I thought could be improved upon. The entry also mentioned a couple of properties for which I could find no proof in the referenced articles/literature.

The proofs for all of these properties, including the upper bound, are not trivial, but also not very difficult, I'd say first year undergrad.

I would like to expand the entry with the improved upper bound, but since I do not trust myself to be mistake-free and I do not expect others to trust me, I think the entry should contain references to proofs for every fact that it mentions, since it is very important these properties are correct.

My question is therefore: where can I publish/put/leave such proofs, in such a way that people who use the OEIS can read them as well (in order to verify it for themselves)? It is by no means groundbreaking work, nor very important, so I don't think any journal (or person reading a journal) would be interested in it, but as scientists and mathematicians, it is always important to give proofs for the claims we do. The only place that I could think of for such a publication is arXiv.org, but I am not sure whether that would be appopriate or not.

  • $\begingroup$ If the proof is short enough, you can post it here. Use the tag "proof-verification". If it's longer, my guess would be that the best thing is to find someone at a university to proof read it for you. $\endgroup$ – lulu Aug 13 '19 at 11:05
  • $\begingroup$ Well... I think it is important that such a proof can be linked to from the OEIS entry, in order for people who use the OEIS to be able to verify that it is indeed true. $\endgroup$ – Tempestas Ludi Aug 13 '19 at 11:08
  • $\begingroup$ So? if you post it here, say, link it to the OEIS entry. Users here are well familiar with OEIS. If people here confirm your argument, you could submit it to the managers of that site. $\endgroup$ – lulu Aug 13 '19 at 11:11
  • $\begingroup$ I don't know if there are guidelines for proofwiki.org/wiki/Main_Page but it might be a good way to put up a proof to have a link the OEIS can point to. $\endgroup$ – Hugh Denoncourt Aug 13 '19 at 13:27

Perhaps you are underestimating your contribution. If so, you could consider the electronic Journal of Integer Sequences: https://cs.uwaterloo.ca/journals/JIS/

Posting to arXiv and linking to that post from OEIS is a reasonable strategy, although it will not get you the proof check you want.

  • $\begingroup$ I did not know there was such a thing as the JIS! I could see if it is publishable there. If not, I might have it proofread by people I know and then publish it on arXiv. The most important thing for me is the possibility for others to verify how someone came to a conclusion, and whether that line of reasoning is valid or not. $\endgroup$ – Tempestas Ludi Aug 13 '19 at 13:13
  • $\begingroup$ I understand the hesitation to put it on the arXiv. There is some moderation at the arXiv and standards they have for content. For example, see arxiv.org/help/moderation and the guidelines they have there. I don't say this to discourage this approach. If the intent is to submit to JIS, I believe the criteria are satisfied. $\endgroup$ – Hugh Denoncourt Aug 13 '19 at 13:23

You have a few options. You could submit a file to be associated with the sequence. You could create a OEIS Wiki page for your proof. You could ask a question here about the validity of your proof. There are other options with varying levels of practicality for placing your proof on the WWW, for example, if you have your own website. You can use a combination of these options over time. Also be aware of the Wayback Machine of archive.org which keeps the contents of websites even after they cease to exist.

  • $\begingroup$ Hm... The thing with my own website is that its persistence is very dependent on me. I.e. if something happens to me (or I get bored and decide to throw it away and create a new one), everything I published there will vanish. $\endgroup$ – Tempestas Ludi Aug 13 '19 at 13:18

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