Her early research 'laid the foundation' [=provided the basis] for many important medical discoveries.
These charges have no 'foundation' in fact. [=there are no facts that support these charges]
The book explains the moral 'foundations' on which her political career was built.
(..) But if we go to the capital, we'll go with two armies, we'll go with three dragons, and anyone touches you, King's Landing burns down to the foundation stone. And right now she's thinking of how to set a trap. Of course she is. And she's wondering what trap you're laying for her. (..)2017 TvShow: Game of Thrones Title: Beyond the Wall Season: 7 Episode 6