Claw of the Conciliator, chapters 1 to 3
There's a gap in the narrative after the ruckus passing through the wall, and Severian is separated from Dorcas and his other chance companions, but is still accompanied by Jonas. He is in the nearby town of Saltus, and employed by the town elders to practice his profession- he is ready to execute two people, one accused of being a servant of the bandit Vodalus. The bandit was sealed in his house, and is dragged from it by a mob after it was battered in for access. Severian catches a glimpse of Agia.
Severian searches for Agia at the town fair. He doesn't find her, but comes across a tent containing a green man- who Severian pays to speak to. The green man is from the future, and chained up. Severian talks to him, and believes he learns that the sun will become brighter in the future. Severian gives the green man the means to free himself.
() The Cathedral of the Pelerines. It was made of silk, and with the bottom lit soared into the sky, like a paper cone. And it sounds like this is by design.
() Severian seems remarkably unconcerned about losing Dorcas.
(*) The photosynthetic Green Man is nifty. I wonder why he travelled back in time. Anyway, that was the point where I started fully engaging with the book- the gap in the narrative, though I knew it was there, threw me.