How is this defined?

1 if you've been emailed or mentioned (cited) by Jeffrey Epstein. 2 if you've been emailed or cited by someone who has an Epstein number of 1, and so on.

I ask because writing a paper with someone is a non secret operator.

I suspect there is no way to establish, if one has an Epstein number >2, what it is.

You have to self report of course. First we find all the 1s then we find all the 2s, and so on