The El-Melloi group and the Crudelis group are sharing an Atlas tent in the second layer, which will be everyone's base from now on. Log was still lying down but could raise his torso with bone tentacles to talk. The stimulant Latio injected is the only thing keeping him awake at the moment. Like his daughter, Log also speaks in the third person. He is the official representative of the Crudelis because the actual family head, Log's father, never leaves to the outside world. Waver has two questions. The first is about the reason to split the suspects in two tents. The answer is as expected, to mitigate the possibility of the culprit killing everyone at the same time but also not allow them too much freedom. The second question is about Atlas's goal in the excavation. Karmaglyph is clearly in it for his academic curiosity, but Atlas is currently excavating a library with past research data when it's practically a duty for them not to know what's going on in the lab next door. Waver questions if the excavation was authorized by Atlas. After a shoddy attempt to deflect with commentary about Waver's character, Log finally starts explaining. He's a superior instructor, so he has the right to take the submarine and the other tools out without any inspection. They can't disclose their personal research, but prying into other people's research without permission is technically not illegal, which is why the Ishtario duo agreed to join. The Clock Tower has its Sealing Designation enforcers on duty, but Atlas has no such force, they just assign anyone available, most often someone not affiliated with the Institute. This generates a procedural delay. Log, Latio, Giuseppe, and Quart are trying to exploit that and take what they need to fulfill their respective research before a proper inspection says they can't. Having learned that, Waver thinks the most likely culprit is either an Atlas spy trying to punish the loophole abusers or one of the 3 Clock Tower mages hired by a dissatisfied Atlas member to do the job. Waver then asks Ptolemy about the guardian. It indeed belonged centrally to the third layer, but the second layer is still part of its patrol route so the attack could have been a coincidence. It's extremely unlikely the culprit lured the guardian there to attack Log since just stealing the key doesn't give them any control. Still, just pointing fingers would only get them killed with time. The El-Melloi and Crudelis then start planning a trap for the culprit.
After Log is recovered enough to walk with a bone cane, the operation proceeds to the next stage. Log had already unlocked the door to the third layer while he was trapped, and now their infiltration team should proceed to map the new area. After that, the intervention team should open the way to the fourth layer. There they would connect to the control room, retrieve the necessary information straight from the server, security key be damned, then book it. The Meluastea and Ishtario were handling the infiltration part since Karmaglyph was the most well-equipped to deal with the guardians' threat and the Ishtario could support with their Atlas-specific knowledge and useful abilities. The Crudelis and El-Melloi would leave the second layer and regroup for the next step after they were done mapping the first layer.
This was a lie. In reality, only Reines and Log will be waiting on the first layer, while Waver, Gray, and Latio would also infiltrate the third layer, setting a trap only the person with the security key would be able to notice. It's clear that the thief's goal is to hinder the excavation, so with the teams being split, they would just hinder one side. And since Latio and Log are the only suspects who know the plan, they can't take counter-measures because that would expose them as the culprit. The thoroughness of Waver's plan reminds Ptolemy of Eumenes, so the two discuss a bit about Eumenes's personality and Iskandar's modern-day fame. Ptolemy is strangely disheartened to learn that his dumb brat went down as one of the greatest kings in history.
The third layer also uses the second layer's crystal pillars as recording media, but here the pillars have grown roots, branches, and flowers for self-defense. Every pillar is protected by its independent decision-making ability, which can override decisions from the central command. Karmaglyph makes a lot of very direct questions about the mechanisms here, and when it starts getting uncomfortable for Giuseppe, Tika explains her boss letting his curiosity get the best of him and running away when it becomes a problem is a recurring issue, although an issue she's willing to paint in a positive light if she gets a 30% salary raise. Giuseppe mentions circumstantial evidence of two previous visits to the Library but believes the previous visitors couldn't read anything thanks to bookshelves' AIs having authority over the then-active security key. One of the previous visits is seemingly by a graverobber group with a history of retrieving lost Atlas property from the outside world. And the other was by Cipher. Checks out with how Cipher was the number one student of his generation, much like Sion is for the generation after his. Quart doubts how much Cipher could have done on his own when the team is struggling this much, but Giuseppe firmly believes Cipher could have reached the fourth layer solo. As for the mapping work they were supposed to do, Quart's Moleculeface leaves a colored trail indicating the path they walked. Further up, the team walks into Ionioi Hetaroi and quickly proves themselves severely outmatched by Iskandar's army, but Karmaglyph understood what the Memory Weapon was about and dispelled with dozens of arrows fired at where the nearest pillar's flower was located in the real world.
Later, Gray's team enters the third layer, finds the other group's track, and goes in the opposite direction. Latio apologizes because she's in the case for personal reasons. She's here to find the truth about her brother's death. Since Cipher died, her grandfather lost his will to get involved with the outside, naming Log as the family representative and becoming a lifeless cog to his research. Meanwhile, Latio was named successor and inherited Cipher's Ergo research. Latio's knowledge about the library's mechanisms also comes from him. Waver asks if Karmaglyph ever met Cipher, because it's possible Cipher created the culprit's key to the fourth layer. If Cipher was killed, the thief could be his killer, depending on how far he got and how much the killer learned from his research. For unexplained reasons, Add is able to sense the right path in the crystal tree maze, so the group decides to follow his lead.
Sion drives Ergo to the desert on a buggy. They pass through
a permanent sandstorm set to hide a secret entrance to the library. Like the Atlas Institute entrance, it's a normal-looking cavern with space distortions inside. Sion wasn't completely trusting her collaborator's intel until she saw the entrance for herself. The secret entrances were made and used for the constructors' convenience then closed down when the library was finished, but this one was reconstructed by the graverobber group. The sandstorm was also set up by the graverobbers to stop other graverobbers from stealing their route. Sion's collaborator told her they had no available means to open the gate, but the gate opened on its when it recognized Ergo. When discussing Ergo as a trump card last chapter, she was being literal about Set being potentially her key to the library.
Immediately past the the gate, there was a falling rock trap. Sion held the rock mid-air with her Etherlite and Rin took this chance to shoot a Gandr. Rin gets past Ergo and closes in on Sion. Ergo tries to explain that he's not being controlled, convincing Rin that he's being controlled into saying that. Sion tries to connect her Etherlite on Rin but can't because of the wind magecraft blowing it away. Sion doesn't understand how Rin is doing this wind in parallel when she's clearly still in Gandr mode. It's because Rin has 3 sets of Magic Circuits. 1 main and 2 subs. The main is shooting Gandr, one sub is doing defensive magecraft with wind, and the other sub using earth to raise rocks on Sion's back. To learn her new techniques from volume 3, she had to learn to distribute the five elements among her sets of circuits, which is what she's exploiting now. Rin hits Sion with a fully charged point-blank Gandr, causing her to dissipate into strings because she was actually an Etherlite Replicant made to deal with traps at the entrance while the real Sion was hiding at a safe distance. Rin and real Sion are ready go all out, but Ergo puts on his mask for Mode Set and turns the whole area into sand except a meter diameter around Sion because he's still locked into not attacking her. While Rin is restrained by the sandstorm, Ergo convinces her he's not being controlled and that the two have no reason to fight.
Rin is caught up on the whole situation offscreen, and Rin and Sion do some tag-team badmouthing of Ergo's goody-two-shoes mediator tendencies and lack of pragmatism. But the girls weren't trying to kill each other anyways. Rin wanted to Sion alive to spill all the information she could offer, while the much more kind and generous Sion was simply willing the let Rin get away with a just a lost arm. Regardless, now the three are helping the search for the Atlas traitor because Ergo needs to learn about himself even if that becomes a problem for Waver. Sion asks if they're helping her because it's what Waver would do, but they assure her that Waver wouldn't help her, he would instead find a better solution that would most likely upset her. Sion is bothered by the mixed messages on whether or not she'll want to meet Waver, but either way, the trio made their decision and crossed the gate to the library.