The Clouded Mountain is the fortress of the Authority. It has been described in chapter 30 in The Amber Spyglass in these words: "Wherever it goes, there is the heart of the Kingdom, his citadel, his palace. When the Authority was young, it wasn't surrounded by clouds, but as time passed, he gathered them around him more and more thickly. No one has seen the summit for thousands of years. So his citadel is known now as the Clouded Mountain."