POSSIBLE SPOILERS
Sorry for that not to mistake anyone the line he said was "I wanted proof you were alive but I failed." Also he appears in the first Liminality he's the guy that says its not over... not yet. He was over Emma Weiland's grave.He also said that he wanted someone to protecet her or something
"I love you. I wanted to create my feelings into tangible. I wanted proof you were alive, my beloved. But I failed. I was mistaken. I sent the message when I found out."
I failed as a father. She is my...our hope. In her lies our dreams. Look after her. I put my trust in you. I wasn't enough. Forgive me, beloved"
Tsukasa flashes to The Sleeping Girl, and tells the Broken Man "He found it." For one brief moment, clarity enters his eyes and he smiles. Then it's gone.
So that is why I think Aura is his daughter.