Waver's group arrived at the 4th layer room because the gates have been left open since Ergo got there. None of the characters know why this is how it is. Sion's group arrives soon after, gathering all persons of interest except Reines and Lob, but causing another round of introductions. This is where Gray learns that Karmaglyph is also the Lord of Mineralogy, and thus Rin's and Luvia's other teacher. The full story is that Kayneth's death caused a clash between the Aristocratic and Democratic Factions to take charge of the department, but Karmaglyph pulled the strings for both sides to lose, and the department fell to the Neutral Faction. Karmaglyph mentioned last volume that Archeology is called the weakest department, but here Waver clarifies that the people still calling it that are people who haven't been paying attention to the Clock Tower in years. Meluastea has been on the rise ever since Karmaglyph became its Lord.
Sion also gets an introduction to the people who still didn't know her. Karmaglyph already knew who she was, the youngest alchemist to ever qualify as an instructor. He knows a lot about everyone, much to their discomfort. He dares a wild guess that Sion was eavesdropping on the whole conversation through Ergo's Etherlite, and since he wants everyone on the same page for the case's resolution, he asks Sion to inject the memories of the conversation in Waver. It's a big shock that he knows she can do that.

Originally Posted by
Karmaglyph
Hahaha. Capable enough for it or not, I'm still the Lord of Archeology. It's our duty to be the number one most informed about the arcana that is outside the Clock Tower. Well... I mean, not counting the Department of Lore, that place is in the headmaster's pocket.
While Sion is injecting the memories in Gray, Rin, and Luvia too, she orients them to focus their mental strength on their identities, because injecting foreign memories can cause them to lose track of who they are. The memory saturation that Sion could induce in them is no different from the memory saturation constantly threatening Ergo. Karmaglyph then goes on a multi-page Melty Blood recap on all the reasons why Sion hates herself. Sion is so devoid of an ego of her own that she can steal memories from others without consequence. She's the ideal Eltnam, an information vampire immune to memory saturation, because she's a borderless outline with no content. He infers that that's why Zepia adopted her. Her nature makes her the perfect Atlas Alchemist. They live by hiding their research because every method to prevent the end of the world is also a method to cause it, but Sion can steal that. The person most qualified to save the world is the monster who knows every way to destroy it.
Sion is demolished by the speech. She's making the face mages make when Waver dissects their magecraft. Not when Waver is nerding out and lets something slip, when Waver is doing it with the intention of hurting them. But unlike Waver's victims, Sion did nothing to deserve it. Rin argues what he did was unnecessary, to which Karmaglyph apologizes, saying he didn't know this kind of thing had to be necessary. With everyone now caught up, Karmaglyph asks for Waver's reasoning on the case, but Waver tells him to finish his own reasoning first. Karmaglyph gets back to his talk about the whendunnit. His lecture presentation is still remarkably similar to Waver's but Gray notes the similarities as intentional on Karmaglyph's part. He already covered Ptolemy at the time of the Library's construction, but the "2300 years ago" period involves 3 groups with different agendas.
Group 1 is Ptolemy wanting to revive Alexander IV.
Group 2 is the Atlas clique who built the library, simply wanting free access to the product of their work.
Group 3 is Crudelis, Wuzhiqi, and Ziz wanting to complete the god-eater experiment and then fight over who gets Ergo.
There's a clear conflict of interest between 1 and 3, but both of their goals require the experiment to be 99.9% complete. Meanwhile, 2 doesn't conflict with either group, but the Atlas rule states that Crudelis can't let 2 know that 3 exists. So Ergo was made in a room invisible to the system in the third layer. That's as far as the 2-3 interactions go.
Now an overview of the 1-3 interactions. 3 feed Ergo the gods and left him digesting them for two millennia. This process is happening on the bottom of the sea to ease up the process of digesting sea gods. Karmaglyph compares these two millennia to the 49 days Sun Wukong spent in the Trigram Furnace after eating the peaches and elixir of immortality. A clear example of Chinese Alchemy, a form of Philosophy Magecraft. 49 days is the time it takes for a soul to reincarnate after death in Buddhism, and 2300 years is the time the trio predicted for an era to live and die. Ergo was in the pod from around the end of the Age of Gods until around the expected end of modern magecraft. Gray likens this to time itself being the god waiting for reincarnation. This comment is so pertinent that Karmaglyph invites her to Meluastea for it.
Flashforward to 2004, a member of 3 would come to take Ergo out of the pod and complete the experiment. That's Cipher. But that would have been a loss condition to Ptolemy, so obviously there was a trap. After Cipher entered and analyzed the room, Ergo's pod was ejected into the sea. Cipher grabbed on to it and that's why he was found drowned. Per Ptolemy's plan, another member of 3 would take Ergo, now awake and conscious, back to the Library to complete the experiment. And as it happened here, the mechanical bird replica of Ptolemy would guide Ergo to the sarcophagus instead of the experiment room, completing 1's win condition.
The stampede of the guardians when Latio was analyzing the experiment room was also an element of Ptolemy's plan. It's caused by an intentional logic error. The experiment room is independent from the library because 2 can't know 3 exists, so when the system detects interaction with a room that doesn't exist, its logic goes kaput. This causes the stampede, which is meant to hold off the member of 3 for long enough for Ergo to be safely ejected from the Library. It's impossible for the system or a manual operator to solve this error because the security key is stolen.
As for why the security key is stolen, that's where the 1-2 interactions come in. Remember Log's infodump about Atlas's procedure last volume. Alchemists are forbidden from disclosing their research but prying into other people's research is a technically-not-illegal gray zone, so Log wanted to do what he needed to and leave the Library before an official inspection reached any decision. The construction of a Library of Alexandria containing copies of every alchemist's research also happened in a similar manner. The Library is too dangerous to exist, so Ptolemy duped the alchemists into creating the security key in his heart as their excuse. After achieving their goals, if they were ever tried for their actions, they can simply show the inspector that the Library is perfectly locked because the security key was mysteriously stolen.
Karmaglyph finishes his reasoning by answering the main question of the Pharaoh murder mystery. How did the culprit manage to leave the Library with the heart? His answer is, they didn't, because there is no culprit. Since this was all part of Ptolemy's plan, all information that came from Ptolemy is a lie. The security key is still inside his mummy, inside the sarcophagus, inside the locked Library. If the theft of the security key is just a pointless excuse for group 2, there's no need to actually carry the heart away. Just make it so that the system reads the security key as stolen when there's an Atlas alchemist nearby.
With his reasoning concluded, Karmaglyph invites Ergo to open the sarcophagus, both to prove the heart is still there and to seal Ptolemy's victory as the schemer who outwitted the other two groups. However, Waver reminds him that after Karmaglyph's turn as the detective was over, it was his turn. Waver has additional reasoning to present.
Waver believes Karmaglyph was completely right about how and why Cipher died and about the Pharaoh murder mystery being a complete farce. The heart must be still inside the mummy. But there's one key element of Ptolemy's motive that Karmaglyph ignored. If all Ptolemy wanted was to revive a guy whose death he felt guilty for, why not Iskandar? Iskandar is another corpse Ptolemy stole, and reviving him would have been the smarter choice as it would put an immediate end to the Diadochi Wars. Ptolemy lived in war, so people meeting tragic fates were a common occurrence to him. There's no reason why Alexander IV was special.
It was established before that Ptolemy created a whole Magical Foundation for this plot, but with this question being raised, "Ptolemy reconstructed a mythology around Iskandar to revive Alexander IV" makes less sense than "Ptolemy revived Alexander IV to reconstruct a mythology around Iskandar". Creating a new god was the end, not the means. The answer to "why not Iskandar?" is that Iskandar had too much of a known personality. He would become a god based on what's already established in the world about him. Alexander IV, on the other hand, is a nobody raised away from human interaction. A blank slate to create whatever god Ptolemy wanted him to be.
That's a theory Karmaglyph also came up with but dismissed because it raised the glaring question of "why did Ptolemy betray group 3?". If all Ptolemy wanted was a new god, then he only needed to let group 3 achieve their win condition. He saw no conflict of interest there. That's where his logic failed. Karmaglyph's mistake was to bundle Crudelis, Wuzhiqi, and Ziz as group 3 when all three of them had their own completely different agendas. Before Waver can explain how the group 3 individual interests conflict with Ptolemy's, Log and Reines arrive, finally reuniting the entire cast of the mystery for the final answer.