I have a paper that has some important work. I recently graduated and am about to work at a top 5 tech firm's AI research division. As part of the interview, they seemed really excited about this work and the results I got. They also work on something extremely similar that I improved on (their paper was considered best-in-class in the space and I'm improving on that). Part of the joining agreement was that all papers submitted post-joining would be from that institution (fairly standard in AI) but I also suspect there will be some "coauthor pressure" from people in the same division that worked on the paper I'm building on.
Is there any way for me to notate that I did most of the work myself (ie. quickly write up a rough draft of the paper and submit to arxiv before I join) or is that not advised?