Warning: Spoilers for The Wheel of Time season 3, episode 5
The Wheel of Time season 3 hasn't formally revealed Liandrin's spy in the White Tower yet, but because of the books, I have no doubts about their identity. The Wheel of Time's third season kicked off with the Black Ajah - Darkfriends who have infiltrated the Aes Sedai - making their big move from within the White Tower. After an explosive confrontation, Liandrin's true loyalties were discovered, with multiple Aes Sedai exposed as traitors who have gone against the Three Oaths.
As discussed in The Wheel of Time season 3, episode 5, it's known that there were at least 13 Black Sisters lurking in the White Tower. However, the Black Ajah must still be operating inside the White Tower, acting under the orders of Liandrin or perhaps one of The Wheel of Time's eight Forsaken. Verin, Siuan, and Leane all suspected Elaida, but she has since been absolved. As a result, the mystery will linger a bit longer in the show, although season 3 already confirmed my suspicions.
The Wheel Of Time Books Indicate That The Black Ajah Spy Is Alviarin
The Wheel Of Time Clearly Emphasized Its First Alviarin Name Drop
During an exchange between Elaida and a member of the White Ajah, the latter was identified as "Alviarin Sedai," with the show even seeming to draw attention to the name. Once realizing that Alviarin was indeed on hand, it became clear to me that she's the missing Black Ajah member. After all, the book version of the character managed to maintain her cover as a loyal White Sister for a long period of time, all the while serving the Dark One. Alviarin was a key antagonist across a number of installments in Robert Jordan's Wheel of Time series.
In her brief appearance in episode 5, Alviarin succeeds in coming across as a somewhat typical member of the White Ajah, and not someone who would be the first suspect in the hunt for a traitor. In the books, of the White Ajah are essentially the historians and the philosophers of the Aes Sedai, with their focus being on the pursuit of knowledge. Alviarin's TV counterpart reflects those interests, indicating she won't side with or against Siuan based on personal loyalties when she says, "the White Ajah sides with no one, outside of reason and logic."
it's more likely that in her effort to stir up conflict, Elaida is playing right into Alviarin's hands.
Alviarin behaves as one would expect from a White Sister. She expresses hesitation when Elaida tries to convince her that Siuan is a weak leader. This isn't surprising, even though an insurrection against the Amylrin Seat or unrest in the White Tower would serve the Black Ajah's goals. After all, the book version of Alviarin also succeeds in maintaining a believable facade, with many characters believing that she was loyal to the cause of the White Ajah for years. Instead, it's more likely that in her effort to stir up conflict, Elaida is playing right into Alviarin's hands.
Alviarin's Plan In The Wheel of Time Books Explained
Alviarin Uses Elaida To Control The White Tower
In the source material, Elaida usurps Siuan Sanche, taking her position as the Amylrin Seat in book 4, The Shadow Rising. She chooses Alviarin Freidhen to be Leane Sharif's replacement as the Keeper of the Chronicles. In the book, Alviarin was vital to Elaida's attempts to gather from the Aes Sedai after Siuan's downfall. Thanks to Alviarin, she had the White Ajah on her side. In playing this role, Alviarin won Elaida's confidence. In turn, she developed a way to control the White Tower without being its official leader.
The Keeper of the Chronicles is second-in-command to the Amylrin Seat and her most trusted confidante.
Alviarin didn't try to become the Amylrin Seat because she didn't need a title to have power in the White Tower. In her capacity as the Keeper of the Chronicles, she organized a failed mission to capture Rand al'Thor, and planned to put all the blame for her mistakes on Elaida. In doing so, she was able to blackmail Elaida and keep the Amlyrlin Seat herself under her thumb in book 6, Lord of Chaos. Unbeknownst to Elaida, Alviarin answered to Mesaana, one of the 13 Forsaken in The Wheel of Time. With Elaida forced to bend to Alviarin's will, Mesaana could effectively pull the strings of the Aes Sedai.
The Wheel Of Time Is Already Setting Up Alviarin's Deception
Alviarin Will Probably Be Elaida's Choice For Keeper Of The Chronicles
Evidently, the foundations for a book-accurate take on Alviarin and Elaida's relationship is already being laid in The Wheel of Time season 3. Elaida has made her dislike of Siuan clear, so it's only a matter of time before she starts actively trying to depose her. When that happens, it can be expected that she'll try to persuade the other Aes Sedai to her as the Amyrlin Seat. That fits with the steps the show is already taking, considering that Siuan has already sought influence with her fellow of the Red Ajah in season 3.
As for Alviarin's place in all this, Elaida picking her to be the Keeper of the Chronicles feels like the most logical for her character in the show, just as it was in the books.
As for Alviarin's place in all this, Elaida picking her to be the Keeper of the Chronicles feels like the most logical for her character in the show, just as it was in the books. Right now, Elaida is trying to get Alviarin on her side in her plan to prove that Siuan is unfit for leadership. Since Alviarin acted reluctant to go along with her but didn't shut down her claims altogether, there's a good chance she's opening the door for Elaida to ask for her in deposing Siuan later. It stands to reason that Alviarin will use this to curry favor; after all, there isn't any other prominent figure in the White Tower whom Elaida could count as an ally.

How Rand Can Be Both The Dragon Reborn & The Car'a'carn In The Wheel Of Time
Rand al'Thor is not only the Dragon Reborn; he is also the Car'a'carn, leader of the Aiel. But how can he be both in The Wheel of Time season 3?
The next phase in Alviarin's plan has also been set up in The Wheel of Time. Elaida previously discussed calling a vote regarding the potential capture of Rand by the Red Ajah, which is exactly what Alviarin winds up orchestrating. If it's botched as badly as the scheme she hatches in the books, she can certainly use this to manipulate Elaida. As for whether Mesaana will be the one behind Alviarin, that remains to be seen. There's been no mention of her yet, but it's theoretically possible she's the sole remaining unrevealed member of the eight Forsaken in the TV series.
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