Where does Cassia decide to get rid of Grandfather's paper and why is it so risky?

In an effort to avoid her father, Cassia goes to breakfast late. She is trying to figure out how to get rid of the paper Grandfather gave her. The best option is at an old library since her paper will blend in with the papers of all the books getting destroyed at the library site. Her father is working there that day. Hiking is canceled due to bad weather so Cassia has some free time to go to the old library. At the library site, Cassia sees her father working. He is an Official and she is happy his job wasn't taken away when he lost Grandfather's samples. She notices another Official watching her father. Cassia sends her paper to the incinerator.