WARNING: The following contains spoilers for Episode 4 of The Detective Is Already Dead, "What I See in That Eye," now streaming on Funimation.
The Detective Is Already Dead Episode 3 formally introduced Yui Saikawa as a new main cast member hiding a deep, dark secret behind her outgoing and friendly demeanor. Throughout the entire episode, Kimihiko Kimizuka had his suspicions about his new assignment, beginning with the fact Yui had received an anonymous letter from supposed criminals who planned to rob her.
The more Kimihiko got to know his new client, the less confident he felt about the true nature of his new case. Too many details simply weren't adding up for him, effectively building up the premise of Episode 4, "What I See in That Eye."
One of the first mysteries revealed in The Detective Is Already Dead Episode 4 is the true meaning of Yui's criminal note. Through deductive reasoning, Kimihiko realizes her family heirloom, the Miracle Sapphire, was never the robbery's target and the criminals were not actually hiding at the mansion. Instead, Yui herself is the real target and the criminals are going to attack when she performs her hit song "Sapphire Phantasm" at the concert. Kimihiko and Nagisa become her pseudo bodyguards, relying on Bat's help to locate any snipers or kidnappers, and successfully protect Yui from harm.
Another mystery unveiled during the concert rescue scene is the secret of Yui's left eye. For her "Sapphire Phantasm" song, Yui performs a specific dance in which she briefly removes her eyepatch to reveal her different-colored left eye. This was the point when Kimihiko knew the criminals would attack, and sure enough, a sniper attempts to take out Yui's left eye with a crossbow bolt. This is when he figures out her eye is the real "sapphire" worth ¥3 billion. But the story behind the left eye dives even deeper.
In the aftermath, Yui discloses her left eye is actually false as she had been blind in that eye since birth. As a result, she was withdrawn as a child so her parents gave her the sapphire-colored false eye to elevate her spirit. As this was one of the last gifts she received from her parents prior to their passing, it means a great deal to her and she retains it as a fond memory. Between inheriting a large fortune and a mansion, the false left eye is the one item Yui fears losing the most.
The final mystery unraveled in Episode 4 is the true nature of the crime that was supposed to be committed. Kimihiko realizes there were actually two criminal targets: Yui’s false eye, and Kimihiko and Nagisa themselves. They were supposed to die in a bomb explosion while guarding the vault in her mansion -- a fate that was averted thanks to Kimihiko piecing parts of the mystery together and contacting Fuubi about getting the bomb disarmed.
Furthermore, Yui knew more about the crime than she let on -- she was actually meant to lure Kimihiko and Nagisa into a deadly trap. What tipped him off was Fuubi never being made aware of the threatening letter. While Kimihiko doesn't believe Yui herself is dangerous, he does suspect she was blackmailed by SPES -- a mysterious organization that's been his and Siesta's enemy for years -- into complying with their crime. He believes her eye is capable of seeing through objects, much in the same way that Bat's ear is able to hear minute sounds from a distance, hence SPES's intent to destroy it.
Little is known about SPES at this time, apart from the fact Siesta and Kimihiko have been on their radar since the start of their journey together. Exactly what type of criminal organization they are and why they have such advanced technology will most likely be revealed as The Detective Is Already Dead progresses.