Open source has no formal definition. There are tons of different licenses. They can be OSI-approved or not.
Edit: I doubt the license for this code is an OSI-approved one with this registration business. But I have not checked and I won't check.
Edit: I doubt the license for this code is an OSI-approved one with this registration business. But I have not checked and I won't check.
I think this is the closest you can come to a "formal definition", short of a law defining the term.
OSI in fact tried to file for a trademark on 'Open Source' in 1999 [1], but failed because the term is 'too descriptive'.
[1] https://opensource.org/pressreleases/certified-open-source.p...