Kumon-mi

Kumon-mi is a fictional, simulated world created by Sensei Prime where the entirety of Lessons In Love takes place. In the real world, the simulation and the girls living within it are housed within the Upside Down House. The current Kumon-mi is actually the second iteration. For more information on the history of the system, see the Full Timeline.

Structure of Callous Kumon-mi.
Very little is known about the first iteration of Kumon-mi. It may have looked like a carbon copy of Calm Kumon-mi in terms of geography, or it may have been based within a healthier version of the old district. Whether there were multiple gods, HOPE or other entities like 61 or the underground world at this point in the timeline is unknown. Concepts like the space war or the walls of the city may have been in place, although depending on the nature of memory alteration and the influence of Callous at this time it may have not been necessary to utilize that flimsy backstory for the state of the world.

Structure of Calm Kumon-mi
The current iteration of the world appears to be centered around Kumon-mi High and is explicitly built for Sensei's benefit. The space war and its implications for the world exist as a handwave to create a walled off city where Sensei can be one of the only men left, surrounded of women. The school is called the "highest point" in the city, although that may be metaphorical in the sense that it's closest to the Concerned God.

The old district appears to exist as a dumping ground for dead or dying things. Nozomu was "buried" here; its possible that as Calm Kumon-mi is built on top of the foundation of the original, Nozomu himself still acts as a key pillar of the world and can't be deleted or excised entirely, so he is relegated to the "recycle bin" of the world. Despite this, he still appears to have significant influence over the entire district and even somewhat beyond.

In addition to the surface world there exists the world "at the bottom of everything", where HOPE and the angels reside. Whether this place exists physically below the surface world or on an entire other plane of existence is unknown. The Room With Clocks and 61 likely also exist here.