I hope the time travel stuff is BS
I think there is way too much foreshadowing for it to be BS. The whole super genius brother thing for one screams sci-fi shenanigans. Also, given the way she burst into tears and completely freaked for little reason when Akira declared she considers her a friend suggests this girl isn't telling the whole truth about what befell Pure and her "amore" in the future. I mean who breaks the laws of the universe just to go back and meet their girlfriend a little sooner?
Something horrible has compelled her to return to the past to change things and from what we have seen that is exactly what she is doing. She is changing the future. That was the whole point of that scene with the conflicting memories after the amusement park. We see her confused by the disparity between her memories of what once was and what is now being rewritten. Most concerning is the fact Pure doesn't seem to remember her "amore" ever telling her she loved her in the original timeline. She altered something in her own past by going back and more specifically by going on that date and it seems to be messing up her mind and making her ill.
This story has tragedy written all over it. Dead mother. Horrible betrayal by her father. Two mentally ill siblings both suffering from serious emotional and psychological damage from the family melting down. Some crazy yandere chick claiming she is from the future shows up and starts crying out of nowhere etc. This one isn't going to be all sweetness and fuzzy good times.
if the time travel was true.
I wouldn't be surprised if pure actually has been through many timelines, repeating her meeting with her amore akarin~ over n over again.