I asked the very same question also at meta.mathoverflow, How to obtain the bibtex item for a question with a program?, it occurred to me only now that it might be a better fit here.
The question is about the "cite" feature available on some (but not all) stackexchange sites, like mathoverflow, math.stackexchange, etc. This question is not about extending the feature to other sites.
The FindStat project encourages contributors to provide references for combinatorial statistics.
I am currently redesigning the way such references are processed. In future, a contributor should only type something like [[arxiv:1234.5678]] or [[MO168885]], without providing any further information. The program then will fetch author and title from the various websites. This was (relatively) easy for the arXiv, but for mathoverflow citations (which occur a lot, by nature of the site), I'm hitting a problem:
Which request should my program send to mathoverflow.net to get the bibtex, which is so well hidden behind the share button.
Rephrased: what I'm after is something analogous to a link like:
which serves the bibtex for arXiv articles.