For my master thesis, I worked on a topic that was new both for me, and my supervising professor. Because of that, we missed a well-known paper of our field, and I basically rediscovered the same idea.
We tried to publish it in two conferences, but it was rejected both times (unfortunately, no one pointed out that the work already existed, it was rejected because of too low impact according to the referees). Currently, it is published on arXiv. We are working on an updated version that includes a reference to the existing paper, and highlights that our results were discovered independently but are not novel.
To make matters worse, I also made a mistake in the central proof, so while the idea is correct, the conclusion needs to be weakened (that was done correctly in the original work).
Now, I am a Ph.D. student working for the same advisor. The paper has not been cited so far, but we will need to refer to it soon in a public report about a software we wrote, based on our technique. Also, my advisor is not in favor of taking down the paper entirely.
I felt bad about this for a while, but have come to terms with it now. While it is a bit embarrassing, I guess mistakes happen and there was no malintent. I am making up for it by doing an extensive literature review now, to avoid making the same mistake twice.
My question is about how to refer to this paper in my CV (or when presenting myself in general). I do have several other papers already, some of them in high-impact conferences with many citations (in a different sub-field). Currently, I have a section of my CV dedicated to those papers. I'm not sure excluding the questionable paper is a good idea, because I don't want to make the impression that I'm trying to hide it. But I also want to make clear that I'm aware of the flaws, in a way that doesn't harm my overall appearance.
The general format of my list of publications is as follows:
[Paper title], [authors], [conference name], [acceptance rate], [number of citations] - Main contribution - Second contribution
I'm thinking about using something like this:
[Questionable paper title], [authors], non-peer reviewed (arXiv) - Independently discovered [known technique]
This would not hide the fact that it's known, but also doesn't put too much focus on the paper. Also, it doesn't stress the fact that it contains a mistake (that would be part of the updated arXiv version). Is this reasonable?
The question also extends to how to present myself to other researchers, when they ask me about prior publications in a less formal setting. My plan was to own up to it, and reply something along the lines of "For my master thesis I focused on improving [topic]. Unfortunately, I missed [known paper] and independently discovered the same results." (again, not focusing on the mistake I made).