About purported P vs NP solutions…I was wondering what if you, sooner or later, lets say, 10 years from now, solve yourself the P vs NP question. Can those authors sue you, claiming they have solved and you "stole" it from them?I view this question as an extreme hypothetical. I don't expect either you or I will settle the P versus NP problem nor do I believe any of the papers posted on the wiki will play any significant role in the eventual solution.
I am most worried about myself too. Cause I am actually reading those papers from them and contributing to a wiki that analyze them. What if those guys decide to sue me? Can they?
We rarely see lawsuits in academics and then only when large sums of money are involved, for example patent rights based on research. The Clay Mathematics Institute Millenium Problems do provide a significant sum of prize money but even in the scenario you outline above, the suit would not be against you but instead the Institute for not recognizing the earlier work.
If I write a paper and later learn of some work that overlaps my paper, I will mention this other work even if I was unaware of it at the time of my research. I could imagine a scenario where I don't believe a paper has any connection to my research and the authors of that paper decided to sue me to acknowledge their perceived contributions. In such a scenario I would not be bullied and hold my ground, though not before consulting the university's lawyers.
On a related note, Luca reports on the status of the Poincaré conjecture, likely to be the first Millenium Problem prize awarded by the Clay Math Institute.