Ashen Imitation

 is a side quest in Torment: Tides of Numenera.

Synopsis
After I was strangled to death by a ghostly woman in the Fifth Eye, I awoke in a new fathom of the Labyrinth. There I met the ghost again. She claimed that women in Sagus Cliffs are being transformed into copies of her, though she doesn't know how or why, and she wants to help them if she can. The ghostly woman asked me to look for women who resemble her, or whose identities are being altered by an outside force. When I find such women, I should return to the Labyrinth and tell her.

Walkthrough

 * You need to track down the women across the city to find out what the Ghostly Woman is and what she needs of you.
 * The easiest of the women to track down is Kiyatawa, down in the Dendra O'Hur Chapel. Talk to her.
 * The next is Avina, near the Fifth Eye tavern. Talk to her.
 * To open the next part of the fathom, you need Seria - she appears after progressing far enough in The Sorrow's Prey quest.
 * After Seria appears, she will produce the Ghostly Man at the probability machine. He will prove difficult to convince without completing the fathom. To do that, you need to find Sigyn in the Government Square or talk to Loss-of-self to unlock the final part of the puzzle.
 * Return to the fathom. Approach the figment and witness another scene, making the ghostly woman realize that she did, in fact, die.
 * Now you can use (Persuasion) to make the Ghostly Man stop his vain labors. If you can't pass the test, you have to find the all five women. He will tell you the shutdown sequence for the probability engine.
 * The final step lies at the Buried Crossroads. Head over there and shut the machine down. As you interact with the machine, a force will stop your hand. You can use (Concentration, Tidal Affinity) to overcome it and shut the machine down. Once you accomplish that, Callistege, if present, will ask you about your actions - clearly in relation to her status.