Sword Art Online: Alicization - 1.12 The Sage Of The Library
In The Sage of the Library, the story pauses to give the audience another exposition dump that provides important details on the background of the Taboo Index. While fleeing from an Integrity Knight, Kirito and Eugeo find their way into a library that is overseen by a mysterious Sage. It turns out this sage is Cardinal, the system regulating every virtual world we've encountered since season one of Sword Art Online.
Cardinal might just be the only other being (besides Kirito) who is aware that Underworld is a simulation controlled from an outside world. I never expected to meet a personification of Cardinal and neither did Kirito, who is shocked to learn that Cardinal is no longer in control of the Underworld as she was programmed to be. Instead, that power now belongs to Quinella, whose backstory is summarized in this episode.
As Cardinal explains, the true purpose of the Taboo Index is to stop any being from becoming more powerful than Quinella, the founder and leader of the Axiom Church (which controls the Integrity Knights). Through a series of experiments, Quinella raised her power in the Underworld as high as it could go and through pure luck gained access to all of the system commands, allowing her to live as an immortal being. Gaining this power ripped control from Cardinal and she's been in control of this world ever since. Most importantly for Kirito, this means that the only way to contact the outside world lies with Quinella, which means a confrontation between the two is inevitable.
This episode also revealed a clue about why Alice doesn't remember her past: during the fight with the Integrity Knight, Eugeo remembers the fighter from a previous tournament and when the fighter starts to regain memories, a purple prism begins to slide out of his forehead. Somehow this prism is connected to how the Integrity Knights lose their memories, though it's not yet clear how the process works.
Given that Rath oversees the entire Underworld, I find it curious that Quinella usurping control has never been mentioned before. You would think an A.I. taking over would be a top priority for the human controllers, which means one of two things: one, Rath is somehow unaware of what Quinella is doing (which seems unlikely), or two, they've known all along and they're hoping Kirito will somehow fix the situation given that he is human and therefore an unpredictable element in the system.
It's not clear where the story is going from here. The library Cardinal inhabits is closed off from Quinella's access but at some point Kirito and Eugeo will have to leave it to keep going. Hopefully the story's direction will become clear before long as the story continues with the next episode Ruler and Mediator.