The tower of wish was a structure that suddenly came into existence, and its appearance marks the second arc of the story.
When it first appeared, so-called "tickets" began appearing over the world, and having one is the requirement to enter the tower. However, one can only use their ticket to join the tower at specific intervals, where the second came a month after the first. There are various ticket colors which bring varying effects, where black is the most valuable and rare one.
When first joining the tower, one will have their stats, and gift effects for that matter, drastically reduced (the more stats you have the greater the reduction), but will be able to regain their stats significantly faster than one would usually gain them. The stats accumulated while weakened will also count toward one's outside maximum stats, so by no means does the tower halt your usual maximum stat gain while trying to regain your old stats. The weakened stats will not remain after leaving the tower, but will be regained at the point you left them at if one re-enters.
It consists of 30 floors, where each floor has its own distinctive feature, and where the final goal is to surpass the final 30th floor. How one gets past a floor varies from floor to floor, and is designed to be a challenge. Each floor has a tower administrator assigned to it, to preserve the desired state of the floor.
Before being sent to progress the floors of the tower, a tutorial will have to be cleared. There are various difficulties of the tutorial. People who used a black ticket can only do the hardest difficulty.
Besides outright beating it, the tower of wish provides a multitudes of possible benefit, like fast maximum stat gain and valuable items. Most prominently though, the tower features a unique skill system where one can learn special skills with unique effects through magic books. There are various categories of skills, and there's a limit to how many you can gain of each.
Players have multiple lives within the tower, but it's also possible to lose multiple lives through one death. Dying within the tower will also cause you to lose skills you earned there. Some floors have harsher punishment for dying than others. (Example there is a curse that can kill even when you have all your lives)