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i almost cried when i read the 1st chapter. my theory is that jade was in love with her, and loved her so deeply and when viche died for his behalf, he was devastated and went to the archdukes to reverse the time and save her. and in order to save her, he made a contract with them. and thats why i think he wants them to be his teacher. i dont know the deal of the contract but thats what i think is happening