Why do I need to claim?
When we were just starting with codebeat, we made a difference between public and private projects based on their visibility settings on Bitbucket or GitHub. Private projects could only be added by premium subscribers, and public projects could be added by anyone. To differentiate between the two, we only allowed public projects to be added using their HTTPS clone URLs, and did not set up the same close integration (setting up deploy key and webhooks, supporting pull requests etc.) we afforded to private projects. This was mostly due to performance constraints that have now been addressed.
Claiming an open-source project is equal to retrofitting it with the features a newly created project would have out of the box: pull request support (including cross-repo pull requests, beat that!), commit statuses, access control, notifications etc. In order to to be able to claim a project, you must own it (have admin access) on the Git provider's side. Also, if you haven't done that already, you need to link your Git provider account with codebeat. This can be done on the Profile page in your codebeat account.
Updated over 5 years ago