When to add a coauthor to a paper I am working on? I am doing a phd in computer science.

Months ago, I was having an informal discussion about my research topic with my advisor, and he came out with a very high level conjecture about my research topic, something like "I have the feeling that A implies B".

Now, I am working with other people on a different project, and during the work for this paper, I realized that what we were doing demonstrated that the conjecture of my advisor was correct (so A do implies B), and this makes a lot stronger our paper.

Now, which is the right etiquette to follow in terms of authorship of the paper?


Should I ask my advisor to join the project as a coauthor because the paper proves what he informally conjectured?
Should I simply speak to him notifying this fact and add him in the acknowledgement?


I have a great relation with him, but I am not sure on how to behave with respect to this topic.
First, yes, you should speak with him. There different ways how to approach him and I would suggest to inform him about your progress (something you should do anyway) and to just ask him how to proceed regarding co-authorship.

In general, merely posing a conjecture does not merit co-authorship, but you could ask, if he would like to contribute to the paper (e.g. by checking/rewriting the proof/statement of the conjecture, providing more intuition as to why this conjecture is true, putting the conjecture in context with references…).