The library court yard
The Library is a one of the damaged buildings of the Nation from the destruction of the Machine War. It was 3 and 4's refuge in due course during and after the war’s end, as presumably the twins ran away from the others with questions always intriguing them and to seek out what all they could data-collect for answers and important input to catalogue.
History
The Library is a historically architectural building harboring many shelves of books, paintings aligned on the walls, and beautiful statues outside alongside a bridge that crosses over a small fountain. A small body of water inside an area of the building has a tunnel in one of the walls that leads to the network of sewers. The Library was also surrounded by many colorful trees and bushes. It also has a gate that allowed visitors to gaze at the Cathedral.
The Machine War
The Library fell prey into the damage of the war between the Machines and humanity. It suffered many harmful blows and attacks from the war.
From the aftermath of the war, the Library is now damaged and moderately unstable. Most of its walls, windows and its roof are now busted, the books inside the building had came off their shelves and scattered the whole floor. The indoor mini lake, however, remains to be clear and not full of sewage. Outside of the Library, the bridge is still standing but most of the statues alongside it have damages onto it (such as a statue's hand being blown off). Plus, all of the trees and bushes have no life because of the war and its poison. The gate was still there, open.
After the war, however, from an unknown part of time, 3 & 4 ran away from the others and ended up here in this building, thus starting their research about the whole world. A few days later, there is a section in the library where 3 & 4 kept every important books that they found important and needed to be remembered.
7 took 5 and 9 to the Library as she realized 9 is like the twins, and that they may know something that he has not known. When inside the Library, it was a mess of books; one painting had hit the ground from its foundation. The stitchpunk twins' section, however, was a bit neat. There was what appears to be a big "scrapbook" with excerpts and pictures from old newspapers or books, ropes were dangling onto it. There was also an installed elevator that percase 2 (possibly 5 as well) and the Twins made, and a jar showing two preserved snakes standing on the far right corner.
After the Winged Beast attack, the whole stitchpunk tribe (except 3 & 4, since they refused to return) came to the Library to recover 7, who was wounded. However, when the Seamstress attacked and left, taking 7 and 8 with it and 2 detached from its tail, the stitchpunks were forced to leave this building, even the Twins. Before they left this building, 5 and 9 gave 2 a proper burial by sending him on a makeshift boat through the sewers.
The Library was never seen again throughout the whole film, but presumably not receiving any further damage to it, it is presumed to be still standing.