A stuck shelf in Clean The Library does not always mean the game is broken. Many stuck moments happen because the wrong book is on top of the stack, the book belongs to a similar shelf label, the shelf area is crowded, or the player is trying to place from a bad angle. Reset the situation before leaving the server.
First, cycle the stack. On PC, use the scroll wheel. On controller, use LT. If you are standing at the correct shelf but the top book does not match, another book in your stack may be the one you need. Cycling before moving is the fastest fix and costs almost nothing.
Second, drop the stack in a readable spot. The game description says all books now save even on the floor, so dropping is a normal recovery tool. Place the pile near the shelf or along the path where you can still identify it. Scattering books in the middle of a walkway makes the reset harder. Once the pile is down, pick up only the target book or a smaller stack and try again.
Third, zoom or reposition before placing. On PC, right click zooms in. Use it to confirm the shelf label or book text if the library is visually crowded. Move slightly to the front or side of the shelf and try the place input again. A small angle change can fix a placement attempt that feels stuck.
Fourth, clear nearby matching books. Sometimes the problem is not the shelf but the mess around it. If there are multiple books or piles near the same spot, finish the obvious matches first. This reduces visual clutter and makes it easier to tell whether the original book was wrong, blocked, or simply hard to place.
Fifth, check whether the book belongs to a different but similar zone. Shelf tools and route notes can help, but the live in-game label wins when it disagrees with a route note.
If the same book still will not place after cycling, dropping, re-picking, zooming, and checking the label, it is reasonable to suspect a live-server issue. Move on to other shelves so the run keeps progressing. Return later with a cleaner area. If the problem remains, rejoin or report the issue through the game's route channels if available. A speedrun route wait until you know whether the stuck book was a route mistake or a real bug.