The TV performances say: Lyrics: PJ, RP-T Track: PJ ---- Not very helpful when googling. The copyright association adds another name: Y-DUCK.

I try searching PJ further on the copyright site (he's got the same ID number as well, so I assume it's the same person), and find him/her credited on various tracks - among them an early IU track - Feel So Good, which sounds nothing like Fat Cat's.

There are pages and pages of songs credited to this PJ, which makes me wonder if it really is one person, but if I read the site correctly it is.