I was given a paper to peer review. A result of that paper has been obtained with some extrapolation trick and so they present it as highly plausible conjecture.
It turns out that me and another collaborator computed the exact same thing (for other reasons) in a work that is still unpublished and we used a method that is rigorous. Our results match so in principle I could prove their conjecture.
Now there are a few things I could do, and I'd like some opinions from you:
- Don't say anything. When our paper comes out I will cite them and say that we prove their conjecture. This is ok, but it itches me a bit to recommend the publication of a result claimed as merely a conjecture when I know it to be true.
- Say in the report "hey, by the way, you could prove your result by doing this. Please do it." However it is a hard computation to set up and I would just make them waste time. Also, I would need to ask my collaborator's permission on this.
- Say in the report "hey, by the way, I have unpublished work that proves your conjecture, so great news." But I don't know what that would accomplish.
I'm obviously leaning towards 1. but maybe some of you have even better ideas.