In your quest for answers, Alphinaud has you proceed to the Archeion in search of the custodian there.
This quest is available if you have completed the quest Glorified Ratcatcher.
Starting the Quest
Talk to Alphinaud in Labyrinthos to begin the quest.
Speak with the Archeion Custodian
Go southeast. You may wish to talk to the Chocobokeep before you proceed. Then go east and attune to the Aetheryte. From there, go south into the building. Talk to the Archeion Custodian to proceed. There will be a cutscene.
Speak with Y'shtola
Go northeast to go outside, then talk to Y'shtola to proceed.
Speak to People Outside the Archeion
There will be an orange circle in the area. Go to the west side of the circle and talk to the Bemused Student. Then go to the east side of the circle and talk to the Bone-weary Worker.
Search for the Pack-Bearing Gleaner
Go northeast to the orange circle in the minimap. You will find Erenville in the east side of the circle. Talk to him to proceed.
Move to the Designated Location
Check on the sparkling destination, then shoot the green bird that says "caw! caw!". There will be a cutscene.
Speak with Alphinaud
Go south to where the orange arrow is pointing in the minimap. Talk to Alphinaud to complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Alisaie to accept the next quest: The Medial Circuit.