Many have thought the Atrium of Time was a place where time stands still, as evidenced by the symbolism of a broken sundial . But in his two trips there, Severian finds different seasons, first winter, then autumn.
I think Mantis in Lexicon Urthus gets closer to the heart of the matter by calling the Atrium of Time "A time travelling structure, like the Last House, located in the heart of the Old Citadel". This is a good comparison, because Severian has to follow a long, twisting, confusing path to find both the Atrium of Time and the Last House. Both times he is following a path marked by guides, Triskele and Mannea. Neither place can be found by taking a short cut (up a cliff, or in a flyer).
What I think is missed is that the Atrium of Time is an open space with many doors to towers surrounding it. The Last House is a vertical structure, that structure being essential to its nature. The higher floors of the Last House are progressively in the future and the lowest floor is in Severian's present. So it is the towers off the Atrium of Time which must be time-traversing structures, not the Atrium itself.
The Last House is probably a Hiero structure, crossing thousands (maybe more) of years of time. The Atrium of Time and its towers are probably a Father Inire creation. We learn in Urth that Inire's Secret House is a poor imitation of the secret ways found in Tzadkiel's ship. So I think we will find that the Atrium of Time towers traverse a much smaller span of time.
I'd like to call the catacombs through which Severian finds the Atrium of Time the Underground Path. Where else might this path lead if explored further? After their first meeting, Rudesind (Inire?) tells Severian that if he follows the armiger's direction to Ultan he will only arrive in the Reading Room. "From there it would take you a watch to get to Ultan, if you ever did". This sounds a bit like the sort of path that takes you to places like the Last House and the Atrium of Time: long, twisting and with guidance needed. Rudesind directs Severian to a shortcut- a room containing paintings with hidden books in them and a downward stairway. At the bottom is the door to Ultan. This suggests to me that Ultan's Library, which extends to the House Absolute, exists in the past. Cyriaca's story supports this.
An Underground Path suggests there is a Ground Level Path. Where would it go? I will suggest it stays in Severian's present and is, in fact, Rudesind's Art Gallery which also extends all the way to the House Absolute.
I think the House Azure is connected in a similar way.
So, what else is suggested by all this? I think it suggests the existence of a Path of Air, which also extends to the House Absolute but exists about 60 years in the future. More on the implications of that later.
Valeria notes that her tower is very old and decrepit and that she "had never gone above the lower floors". If there are basement levels to her tower then she lives in the past and present. The antique quality of her name, clothes and furnishings support this. Severian notes there are other decayed towers, notably, the Witches'. So apparently it is these old places and not the spaceship towers which are time structures. What are the screams and colored lights coming from the top (future) of the Witches keep?
When Severian visits the witches he climbs several stairs and a ladder made of saplings lashed together he finds the Cumaean, (in the future), looking through her glass table at the artificial landscape with hairless crippled animals. My "The Wtches Function" post offers some suggestions regarding this.
Severian climbs another, similar ladder of lashed wood also associated with time bending. A long, twisting path is travelled to get there. It is at the Jungle Hut. Agia has never been that deeply in this garden so I think Father Inire, as designer, is acting as guide. Here in the Jungle Hut we find, in Robert, and Marie and an airplane, a place most similar to our own, the readers', world though it seems like a movie scene, perhaps from Gene Wolfe's youth. Because Severian has to ascend a ladder to get there, it is suggests that our Earth is in the future of Urth.
-bsharp