The first thing Karmaglyph asks before the reasoning can continue is how Log and Reines got to the server room.
- Ptolemy and Ergo came through the space foam.
- Karmaglyph, Quart, Giuseppe, and Tika arrived because Karmaglyph analyzed a bubble and made their passage.
- Waver, Gray, and Latio had Add successfully calculating their way through the labyrinth because he's a more advanced Atlas product than anything in the Library.
- Sion, Rin, and Luvia arrived by tracking Ergo's Etherlite and using Luvia's graverobber routes.
But as far as he knew, Reines and Log didn't have any similar means of navigating all the way from the first to the fourth layer.
The answer: Log found the way by reading Cipher's research data. That data that Karmaglyph went to an underground auction for but couldn't afford. It turns out the winner of the auction was Reines. They had the data stored in Trimmau for over a year, since long before they met Latio and found any use for it. 2006 Waver obviously didn't know what Cipher's research data was about or how to browse, but he still made a point to win that auction despite his financial situation because Karmaglyph demonstrated too much interest in it. Even if Waver didn't know what the auction prize did, he trusted that it was something useful if Karmaglyph wanted it THAT much. And this gamble paid off now with Log being there to read the data for Reines.
Back to the reasoning. Waver believes Ptolemy was outwitted by the AoG Crudelis. It's incredibly suspicious that the alchemist would simply let himself die, when the Atlas law forbids him from sharing the Ergo project with his descendants, while Wuzhiqi and Ziz were both staying alive through the 2300 years they needed to see the project's completion. There has to be some trick there. Logically, the AoG Crudelis should still be in the library. Since the library is programmed to fake the security key's disappearance if an alchemist is nearby, he would need to wait the 2300 years inside. And Cipher's death was an intentional sacrifice, as he couldn't outsmart Prolemy's trap so needed a successor to fall for it in his stead. Waver claims the Crudelis guy is the one actually in the sarcophagus, ready to surprise attack Ergo when he opens it.
So now it's time to check the final piece of evidence and solve the case. Log uses the cheat codes in Cipher's data to open the sarcophagus in Ergo's stead. He does his Exoform Acoustic Mode like Latio in Ergo's research room in the last volume and opens the sarcophagus. When he does, Latio jumps at him with her bone sword. It doesn't pierce him because he's wearing Trimmau as armor, but it sends him flying to the wall.
Battle against Latio and Tangere. Tangere doesn't want to be the enemy, but since he's Latio's familiar, he has no choice.
Latio is making a totally non-villainous face. Waver infodumps on the default Atlas abilities to explain Latio's betrayal while Rin's healing magecraft makes Log at the very least not die.
Atlas's one law is that you can't share your personal research with others, for reasons already explained in previous chapters. This law causes the major problem of each alchemist being stuck with their own perspectives in their search for a way to save the world. And the solution to that problem was establishing Thought Partition as a default alchemist ability. Thought Partitions are separate selves one can share their research with, enabling them to run multiple tasks in parallel and bounce ideas off with. The main advantage of that is having a companion who shares your knowledge and values, but since that doesn't help escape your personal limitations, it's also possible to produce Thought Partitions that simulate other people's values and perspectives. Examples include* Latio simulating her brother's personality in Tangere, and Quart's example of Atlas friendship**.
* Obvious examples not mentioned in the novel would be Sion simulating Riesbyfe, and the Nemo series.
** Atlas friendship is a thing mentioned in chapter 1 that I couldn't fit in the summary and forgot to mention later in the thread. Remember how Quart attacked Karmaglyph in Chapter 1 over his suspicion of Karmaglyph taking Cipher's research data in the action? His motive there is that he considers himself Cipher's close friend despite them having barely ever talked irl because a lot of Atlas friendships involve an alchemist simulating the good times the two could have had together under more normal circumstances. I think that's a really neat call back to how Sion really knew almost nothing about Ries and still made Ries her closest companion.
Anyways, back to the reasoning about the Crudelis guy from 2300 years ago. His real trick to being present at Ergo's awakening was to upload his memory and personality data to the Ergo room walls and have that data invade his proper heir when they entered the room. And as Karmaglyph mentioned in the last chapter when dissecting Sion's character, most people can't take other people's memories because they'd lose track of their identities. 3 years ago, Latio and Cipher entered the room and Latio's Partition #1 got mixed with her ancestor. #1 sacrificed Cipher to get rid of Ptolemy's trap, then forced Partition #2 to run Latio's pre-takeover personality unaware of the Library events so her family wouldn't suspect her personality changed. All this time, the Latio we've been interacting with was #2.
Waver figured this out at the end of the last volume when Latio was struggling to read the Ergo room walls. She was clearly failing to use her functions properly, so Waver advised her to do a self-check. But instead of doing that, she read the wall by doing a performance boost to the point she was crying blood. This meant Latio's main frame really wanted to avoid a self-check at all costs. Presumedly because that would make #2 realize that she wasn't #1.
Reasoning concluded. Tense silence soured by Karmaglyph's out-of-place applause. Latio #1 confirms everything and opens the coffin, saying she'll feed Ergo with its contents. The black miasma inside the coffin attacks Ergo. Sion restrains Latio with Etherlite for breaking the Atlas law, but her Etherlite gets frozen by Karmaglyph's arrow.
Karmaglyph is taking Latio's side because the Lord of Archeology lives to give value to what's ancient. Ergo is from the Age of Gods, so no one in the Clock Tower, not even Waver, is capable of using Ergo to his best potential, so he belongs with Latio, who can make him shine the brightest. He attacks Gray with a barrage of elemental arrows. Even if the Grim Reaper blocks the arrows, she still takes the heat/cold/electric shock damage. Some of the arrows she dodges are homing, returning to attack her. The arrows that don't home at her go draw magic circles on the wall behind her. The circles drawn on the walls shoot magical bullets targeted at Waver, but Rin and Luvia hit those with Gandrs. The fights split into Rin and Luvia vs Karmaglyph on one side and Gray vs Latio on the other.
Karmaglyph's fight is happening by the door so no one can leave. Latio's fight is around the coffin where Ergo is getting trapped in the black miasma. Latio can't step away from the coffin while it's releasing the miasma, so Gray is fighting only Tangere. Meanwhile, Waver and Latio talk about the AoG Crudelis's motive.
The main problem with Atlas is that methods to save the world can easily be converted into methods to destroy the world. But this only happens because the person converting the tech has the same intellectual level as the alchemist who created it. So the AoG Crudelis resorted to assigning tasks to gods. A god's superior intellectual level could create solutions people couldn't even begin to comprehend, and thus wouldn't know how to turn into a threat to the world. He fed Ergo gods to turn Ergo into an Authority computer that would produce solutions beyond human understanding to multiple threats to the world.
The secret Library of Alexandria is relevant to this because it contains registers for all problems Atlas was facing 2300 years ago. So the goal was to use Ergo to produce solutions to all 2300-year-old threats, clearing the Library's backlog in one fell swoop. Ergo's body obviously wouldn't survive, but that's good for Crudelis. He wanted Ergo to be a one-off solution because if the god computer wasn't self-disposable, he'd also be another Atlas product with the risk of becoming a world threat.
Quart and Giuseppe are out of the fight because they agree the AoG Crudelis was doing the right thing. It's part of the reason why Karmaglyph is fighting on her side too. But Waver does a repeat of his "that's no reason to give up a student" speech from volume 1 when Latio #2 tried to say the same thing.
Meanwhile, Tangele is fighting Gray with a bone armor full of cannons, but she's handling it since she can imitate Rin's bajiquan a little. She can even pull off some tosses on the bone giant. By the way, the energy source for the Ergo computer is Alexandria's underwater volcanos, which Latio #1 already activated. Countdown of 27 minutes and 56 seconds until the eruption.