you need wait until someone anounce that pyra is waiting you and then after 2 times visiting pyra the peitho story ends because is not complete so you need wait (try to save the game and load it after complete leila training)
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did you already finish leilas train the public, private because the anouncement is the last part for now i think you should save and load the game it works for me to get the anouncement i dont remember if you need to talk or train for a few moments, or wait but after you meet pyra and try this 4 ways: train public or talk with she or wait or then save and load that game.