I’m a junior researcher in CS and this happened to me when I was an undergraduate. To simplify a bit, people are interested in the values that s(f) can take on, where f is a function. There were essentially two known functions that tied for the record for “smallest value of s(f).” I came up with a methodology that lets you construct way more examples, including multiple, unrelated infinite classes of such functions. I also showed how to construct a function with certain desirable properties that also tied that record. I then made a couple conjectures.
I put the paper on arXiv and worked on my conjectures. The professor who was my mentor (but not a co-author) got really busy because he made a travel-the-world-lecturing level breakthrough and my paper fell by the wayside in terms of his priorities. Also, I graduated and took and industry research job so I simply had less time to think about my paper. About two years after I put the paper on arXiv, I get contacted by a conference asking me to peer review a paper. This paper proved some of my conjectures (which I had done, but hadn’t written up), disproved others, and broke the record for the smallest value of s(f). They cited us and credited us with bringing the question to their attention.
Their paper got published and mine still hasn’t. My research mentor hasn’t been very encouraging about publication at this point, about four years after the research was done. From what I understand, there’s no real reason for someone to publish our paper now, except historical interest. I don’t know of any journals that accept “legacy submissions” of unpublished papers that have already been read and advanced by other work. I think the arXiv pre-print has two or three citations now. A side project right now is to combine some of my ideas that didn’t get preempted with new ideas I had after reading their paper (and a few others) into a paper that I can get published. It would be nice to get something published out of my old research.
My understanding is that, unless it’s a monumental result, when this happens you take the loss and call it an unpublished preprint. From a resume POV, I got a little luckier than that: I presented a modified version of the results at a peer-reviewed undergraduate research symposium. The purpose of the symposium though is to help undergraduates who do research have a second set of eyes going over their papers before “real” publication, and it’s expects that most presented papers would get published in journals or presented at “adult” conferences.
As I said, I’m a junior researcher and it’s quite plausible I’m wrong. But this has been my experience. If anyone thinks they know a venue that would be appropriate for my paper, I would love to hear about it. If anyone’s curious about the paper, the problem is the Sensitivity Conjecture and you can find my paper here.