The comic book store owner Stuart seems interested in asking Amy out. He asks Leonard to check if this would be okay with Sheldon, who dismisses the notion that Amy would be interested in Stuart. When Stuart and Amy do begin going out, it calls into question Sheldon's stance on their relationship, forcing him to finally categorize her as his girlfriend ... complete with a Relationship Agreement.
This Episode's Science
Howard: I thought you didn't like Facebook anymore.
Sheldon: Oh, don't be silly. I'm a fan of anything that tries to replace actual human contact.
Sheldon: I present to you The Relationship Agreement, a binding covenant that in its 31 pages enumerates, iterates, and codifies the rights and responsibilities of Sheldon Lee Cooper, here and after known as "the boyfriend," and Amy Farrah Fowler, here and after known as "the girlfriend."
Amy: It's so romantic.
Sheldon: Mutual indemnification always is.