Missed a citation which has a solution to the problem that I worked on

Question

About 4 years ago, before I started my PhD, I published a paper which used a method to improve an existing result. There were 2 papers on the existing result and method which I used for my work and appropriately cited. A couple of days ago I discovered another paper on arXiV by the same authors, which dealt with the same problem, which I did not cite for reasons I can't remember. Also, I realize that they address the same problem that I worked on, in a small sub-section of their arXiV paper.

Based on the references that I used, I gathered that the problem I solved had not been looked into in the works of theirs that I cited and made a statement about this fact. Although, the method that I have used is different from theirs, it still makes my statement erroneous. I feel that I am thoroughly screwed and the damage is irreparable. How do I go about resolving this issue? I am willing to let everybody involved on my paper know about it, including the authors whose papers that I have not cited. Is there anything more to be done?

Answer 1

It's difficult to tell precisely as a bystander, but this just doesn't sound like a particularly serious inaccuracy. From your description, your previous publication make no claims about the other authors' paper you've more recently found.

I realize that they address the same problem that I worked on, in a small sub-section of their arXiV paper.

So you missed a small sub-section of a preprint in your literature search. This type of thing happens all the time, at least in my part of math. Yes, you could wish that you had spotted it, but it sounds like your method was still a novel approach to the problem. You're certainly not "screwed" with "irreparable damage" to the paper.

If you like, in the future you can add a bit of hedging to novelty statements going forward. I sometimes include this kind of language:

To the best of the authors' knowledge, the method we will discuss here is the first to solve the problem of fizzing buzzes.

In the grand scheme of things it actually doesn't matter, except in acknowledging that literature searches are hard and that you haven't intentionally neglected something a reader or reviewer happens to know about.

Answer 2

I am assuming that when you say published, you mean published in a peer-reviewed journal. On the other hand, the paper you found was not published. It was on ArXiv. I argue that because of this, you should not feed bad at all. You weren't scooped, since that paper wasn't published.

ArXiv is a non-archival venue. There is no peer-review process, and some academics (myself included) are extremely wary of citing ArXiv papers that haven't been published elsewhere. If they were published elsewhere, I cite that version, not the ArXiv version. The main purpose of ArXiv in my opinion (which is how I use it), is to make your work accessible to a broad audience. Some folks treat their ArXiv papers as published, and expect to receive academic credit for them. I disagree with this viewpoint on a moral/ethical basis, as it undermines the entire purpose of the academic publishing process.

Now, let's pretend that the paper was published and that you simply missed it. Is it truly identical? It seems very unlikely that the result, method, techniques, everything is the same.

I wouldn't worry about it. Let me tell you a story that happened to me not too long ago. We had a result (call it A) that we wanted to publish. When we were in the process of submitting it, a paper with a result B was "published" on ArXiv. Result B generalized our result. However, given the argument I made above, we went ahead and submitted our work, and it got accepted. Later that year, another result C, was published in another venue, which was a special case of our work. They were all valuable contributions in their own way, even though the only one that "mattered" was Result B (the most general one). Joke's on them though - we published an even more general result earlier this year!

This is how science works. We build on each other's work, and if a topic is interesting, you'll have a lot of duplications. As long as you're operating in good faith, citing sources appropriately and acknowledging effort, you're doing it right.

Answer 3

Personally, while not a huge issue, I do feel like other answers are downplaying this a little more than it should be. In some sense it has become a chronic issue, to the point where I feel more than half of the results I see have been done before and few people in the field seem to have any idea that it was done before. Reviewers don't notice, colleagues are excitedly talking about the novelty of the approach, etc... and I'm like, "but xxxx did this back in the 30s." The harm isn't in this happening once, it is that over time entire fields seem to suffer a collective loss of memory.

So while I wouldn't beat yourself up about it, it might be worth publishing an erratum as a service to those that come after you trying to determine the novelty of their own work (they might be reading your work and not have seen the other one yet, and then may never read the other work). Of course with the caveats that 1) the journal you published in is amenable to such minor corrections and 2) your field and coauthors are similarly amenable to the idea. Personally, I respect authors willing to correct their works more than those that do not, but I admit that I know others that view any sort of correction, no matter how minor, as a black mark on the work.