It's official. Paula Abdul will remain on American Idol despite a sex scandal that threatened to knock her out of her judge's chair for good. The Fox network says they investigated the claims that Abdul had a sexual relationship with a contestant in 2003. But the network concluded that there is no proof that Paula was involved in an inappropriate affair. (Hmmm. I guess the phone records and voicemail messages didn't make a bit of difference.) Paula may still be on board with American Idol, but the star has backed out of a new job as a regular contributor on Fox's So You Think You Can Dance. Paula says she is too busy to work on a second show.