http://steamcommunity.com/sharedfile...?id=1115077162
According to this screen, building the library will reduce corruption, but not increase law. There doesn't seem to be a difference when I move the governor out, so it isn't his traits.
I checked with process_cq Thospia, and the library did indeed reduce corruption when finished. But I didn't see an increase in law until I tried building a shrine of Ahura Mazda (which provides +1 law). Looking at some of my other settlements, I found one (Asaak) with 25% law - it had a learning center (+3), temple of AM (+2), and a governor with good traits (+8). Moving the governor out dropped the law bonus to nothing, so it seems like the settlement had a hidden -8 law penalty??