This is my first post, so please let me know if I made any mistakes.
I am applying to math phd programs this year, and one of the things I encountered is that for multiple schools, they ask me to list publications if I have any. I have a paper currently recommended for publication by a peer-reviewed journal(it's on arxiv and thus accessible to public), but it's not strictly speaking accepted. Since usually I get an entire text box to fill in my answer, what I did was that I list my paper, the arxiv link, as well as it's status that it's recommended for publication in that textbox. The status I listed in answer to the question should make it clear that this is not yet published or accepted in this peer-reviewed journal, only that it's "highly probable", and that it's available on arxiv.
I was wondering if my approach here is ok. I am an honest student, but I also really want to emphasize that I have this paper which has been recommended somewhere along with the application other than just on my CV. One of my recommenders have also suggested that this should work.