Now that Alexander IV is really relevant to the plot, Gray and Latio ask for a Waver lecture on his history. Waver provides the real-life biography and touches on some points that are recontextualized thanks to the information we know about Ergo's origins.
1) One notoriously tragic part of Alex IV's life is that when he was Cassander's prisoner, he was cut off from texts. But knowing Ergo's abnormal language learning ability, Cassander's seemingly pointless act of cruelty gains a plausible reason. What if that doesn't come from any god? What if Alexander IV was born with the talent to read anything without having to study the language? That'd be enough of a reason to keep the books away from the kid.
2) Ptolemy's actions in life are another point of interest now that his involvement in Ergo's project came to light. Namely his myth reconstruction. His stealing Iskandar's corpse and controlling his priests to make Iskandar known as both a son of Zeus and a son of Ra sounded like pure fanaticism but now Waver can see a pragmatic purpose to it. Even in the Age of Gods, mages couldn't do anything. Some rituals required the power of a king. Take for example the creation of the calendar and how much that enabled time magecraft. By establishing his syncretic Hellenism centered around Iskandar and uniting all tales and wisdom in the Library of Alexandria, Ptolemy reshaped faith in a way a mage could never. He created a new magecraft foundation that facilitates the mixing of gods from different cultures, and through that, he enabled Ergo's ritual.
But these reveals don't change anyone's motivations. Waver still considers Ergo a student. Gray still wants to live up to the big sister figure Ergo sees her as. On that topic, Gray asks Latio about her past relationship with Cipher, for advice on how to be an older sister. Latio explains her relationship with Cipher is still very much present. Back when Cipher's body was discovered 3 years ago, Latio was too deep into her Atlas research, meaning she didn’t have the time to mourn her dead brother. So she made it so she didn’t lose her brother. She took Cipher’s skull and used it as the core of Tangere's personality. The reason why Tangere always calls Latio "Lady" and the reason why Latio hates it so much is that Tangere doesn't have Cipher's memories, so he doesn't consider himself her real brother.
Flashback to Ziz gathering together with Wuzhiqi and the old Crudelis mage in the Library room Waver's group is currently at. Ziz jokes he's surprised everyone is here, as he was expecting at least one traitor. Wuzhiqi casually tries to punch him, saying he'd be the first one to betray the project. The punch stops before hitting Ziz because he plasters the concepts of delay and stagnation on the space in front of him. The trio then proceeds to announce their contributions. Crudelis provided the location. Ziz devised the spell. And Wuzhiqi found the vessel. In cue with Wuzhiqi's part, Ptolemy entered the room carrying Alexander IV's lifeless body.
Ergo wakes up in the 4th layer's control room. The replica version of Ptolemy doesn't have the clearance to enter the control room even through the space foam, but they got there using Ergo's credentials. Ergo asks for confirmation that he's Alexander IV but the bird can't say for sure, since he can't access the parts of the real Ptolemy's memories that contain Atlas secrets. He took Ergo to the control room because it was always the first place Alex IV would go to. All of the library's mechanisms are designed to let only Alexander IV pass to the 4th layer. The bird guides Ergo through a secret route, trusting that in one of the memories he can't access, the living Ptolemy left a plan to prevent Ergo from being consumed by the gods he consumed.
Rin and Luvia discuss the secret routes the old Edelfelt used to rob the library and conclude that it was a route intentionally installed by Ptolemy for whatever his intentions with Ergo are. Meanwhile, Sion managed to connect her Etherlight communications with Ergo.
While Ergo is following Ptolemy through the secret hallways, Sion instructs him to stall Ptolemy with long conversations. Ptolemy leads him to the core room with his sarcophagus. Ergo tries to touch the sarcophagus to access its knowledge. He wants to know to avoid his memory saturation, he wants to know who he is, but most of all, he wants to know what's the deal with Ruolong. Sion telepathically yells at him to stop but doesn't directly restrain his actions. Ergo ultimately stops before touching the sarcophagus to talk with Ptolemy as he currently is, since he doesn't know if he'll still be himself after recovering his memories. Ergo's question is what Ptolemy thinks the reason for the theft of his heart is.
The running trio celebrates Ergo not screwing this up. During the run, Rin asks if Sion isn't tired from having her Etherlite constantly connected. Sion finds the question absurd. A Six Sources alchemist getting tired from using their Traditional Feature makes as much sense as a normal person getting tired from their heart beating all the time. Sion assumed it was the same thing for Clock Tower and the Magic Crests, so Rin has to lecture her about all the bad side effects of Crests (no new information here, surprisingly). After some more banter, Sion has a moment of pause and introspection, noting how easily she's having balanced conversations now. She was always feared for her Etherlite, but here she was having an easy time, which she associates with the two girls being students of the infamous Plunderer Duke, another mage known for stealing information. Rin invites Sion for an Alexandria tour after they get Ergo out of the Library.
Ergo keeps stalling for time with his whydunnit questioning, resorting to some 6 pages of silly nonsense reasoning, like how the sarcophagus counts as a second locked room within the locked room since
it's sealed shut by chains of lighting. Ergo's stalling tactics paid off, but the goal was to buy enough time for Sion's group to arrive, and instead, it was Karmaglyph's group who arrived first.
Karmaglyph's group reached the 4th layer because all the bubbles he kept making with Gemini to make his portal had the data used for Ergo's warp. The people in the room exchange greetings despite already being in the know about each other through their own channels (the data in Karmaglyph's space foam, Ptolemy's instructions from Latio, and the character profiles uploaded to Ergo's brain by Etherlite). Karmaglyph expresses special respect for Ptolemy since his bloodline's origins lie in the (historical version of the) Library of Alexandria. With the introductions out of the way, Karmaglyph proceeds to present his answer to the mystery.
Karmaglyph fancies himself as a fan of Lord El-Melloi II, so he gets serial reports on all of Waver's cases. For that reason, he's aware that Ergo's case involves Divine Spirits and the Wandering Sea. Though since Ergo hasn't been designated for sealing yet, he's confident he's still the only other Lord who knows about him. Anyway, generally, the key to cracking cases lies on the whydunnit but with those potentially time-traveling factors at play, Karmaglyph's attention moves to the whendunnit. He lists 3 opportunities for the crime to have been committed: at the time of the Library's construction, during Cipher's invasion 3 years ago, and during the joint excavation. The heart could have been stolen in any of these opportunities, but not in any of them there was a need to create the locked rooms, neither by sealing the sarcophagus nor by re-locking the 4th layer. Karmaglyph deduces that in each timeframe, someone came to the room for some different purpose, and this crime scene is only complex because they were trying to investigate the three simple visits as a single thing.
He starts with the first one, on the construction. In a dark version of a Waver lecture, Karmaglyph explains Ptolemy's involvement in the Diadochi Wars, accusing him of his contributions to the start and prolongment of the conflict, thus indirectly accusing him of causing all the tragedies of Alexander IV's life. The guilt Ptolemy feels about it is visible through the mechanical bird. His stealing Iskandar's corpse was a political move to justify his hegemony but stealing Alexander IV's corpse served no similar political purpose, so Karmaglyph reasons that Ptolemy stole Alexander's corpse for personal reasons. To bring him to the library where he'd become Ergo.
But before this heartless dissection of the motive can continue, Tangere opens the room's gate for Latio, Gray, and Waver.