Errata

Stealth checks have been simplified and there's no longer a need to "roll under" when you take risky action (which leads to all sorts of wonky math).

Instead, you establish a stealth score as expected (d6 + Deft + Skill), and that TN travels with you as long as you don't do anything risky. Sneaking across the library while moving silently in this way leaves patrons unawares, but maybe when you get to the stacks where the magic tome is located, you discover it's really heavy. So you need to silently slide it off the bookshelf. In this case, you would make a separate check to deal with that challenge (for example, a Mighty check vs. a TN unopposed). If you fail, you're "detected," which means others in the library are alerted to your presence, and you lose your stealth score. Now you'll need to switch strategies to sneak out of the library. Maybe you decide to impersonate the librarian?

Another way to look at this: suppose you've found the book, but the librarian is standing nearby with his back turned to you. In this case, when you try to pilfer the book, the GM might call for the librarian to make a Perception check vs. the TN of your stealth score (as the librarian has stats of his own). If he succeeds, maybe you dropped the book with a loud thud, and all he has to do is turn around to discover you, in which case you're immediately "revealed." If you succeed, it might mean he looks in the wrong direction for the noise. Nevertheless, Perception checks to detect you for the rest of the scene are made with advantage, since the librarian knows something is up, even if he doesn't know it's you.

(Special thanks to Jon, Courtney, and David for some late night brainstorming on this one...)