The "Dental Hygienosphere" was a tooth-themed amusement park built by Phineas and Ferb, and the main objective of Buford's deal with Candace: to make sure it didn't dissapear. Buford managed to keep it under control for most of the episode, up until Doofenshmirtz's latest inator caused the amusement park to start to go to the orbit. Not giving up, Buford attached himself and then went up with the amusement park.