I am in charge of the MathOverflow backlinks at zbMATH Open and can explain how we fetch them:
We are using a small Python script, which uses the Stack Exchange API, to get all question, answers and comments citing some zbmath document on mathoverflow.net. We use urlextract and regular expression to extract links to zbmath.org.
The script runs once a day. The links that were found are inserted into our database and displayed at zbmath.org with a delay of usually one day. So in total there is a delay of two days from linking to a zbmath document in a MathOverflow post and the display of the backlink on zbmath.org. (It is possible to reduce this delay. We thought this is not needed.) Revisions of old posts are also considered.
Once in a month we run a script to remove invalid MathOverflow links or backlinks to MathOverflow Posts, in which the corresponding zbmath link was deleted. It would also be possible to run this deletion script every day. As we observed that it does not happen that often that backlinks have to be removed, we decided to run it only once in a month. For more details, see
Müller, Fabian; Schubotz, Moritz; Teschke, Olaf, References to research literature in QA forums – a case study of zbMATH links from MathOverflow, Eur. Math. Soc. Newsl. 114, 50-52 (2019). ZBL1428.68357.
As @DmitriPavlov and @TheAmplitwist noticed, links with ?format=complete or using the old zbmath domain zentralblatt-math.org are not recognized by our script. This is a bug that we will correct.
Regarding the original question: There is no policy on formatting links in order for MathOverflow posts to be tracked back in relevant zbMATH Open reviews. We recommend to use the “Insert Citation” button (only available at mathoverflow.net, not on meta.mathoverflow.net). Using this button one can search for a citation string and gets a list of up to three relevant zbmath documents. If the correct document is among the three results one can choose the correct one and the citation will be inserted correctly formatted into the MathOverflow post. However, also links that were pasted by hand should work as long as the zbmath identifier (zbl number or jfm number) occurs in the link. For example,
does not work, but
To make sure the link is recognized, I would advise to use the format zbmath.org/?q=an:<zbl id>. It is also possible to link to several zbmath documents by separating the individual zbmath identifiers using ‘|’. For example:
If some backlinks do not occur on zbmath.org after two or three days, you can write a mail to firstname.lastname@example.org and we will investigate the problem.
Furthermore, we are working on linking to more websites that are interesting for mathematicians. We started with the Digital Library of Mathematical Functions and will include The On-Line Encyclopedia of Integer Sequences (OEIS) in a next step. If you want other websites or services to be included, you can also write to email@example.com.