A Hyperverse is a simulation of Xenoverses or other Hyperverses. Hyperverses have 3 or more layers of simulation and are a blanket term for all simulations above xenoverses. The highest-layer hyperverses are created by Type 9.0 Civilizations that preside in the Kiloverse, the smallest natural verse, while most lower-layered hyperverses are created by late-stage K8 civilizations inside the higher-layered hyperverses.
The civilization that operates our hyperverse is called the Illuminati, a relatively small K9 civilization that is highly balkanized into millions of city-states across their Kiloverse. The original Kiloverse of the Illuminati civilization was deleted in a war with another civilization approximately 50 years ago, so the survivors had to migrate to another kiloverse and used a cloud backup to restore the hyperverses. Since these simulations are imperfect projections, naturally, if you would go through the virtual Archverses within a Hyperverse and through another Hyperverse within the Archverses 1 million times, then you will eventually end up at the Undefinedverse. Hyperverses are frequently deleted in natural disasters that occur on their containing Hyperverses or Kiloverses so entities will commonly keep backups of them.
Some Hyperverses are bigger than their own. Only because of how many different Virtual Realities they contain because of their Xenoverses and Metaverses. In fact, If we're talking about Simulations again, There could be Metaverses bigger than Xenoverses. Which is actually complicated. If only they weren't good at balancing themsleves. That's why the Beyond Abstract entities aren't worried about collisions.