Sorry man, it's a nice theory and all, but she really was just talking about a few times they've met in passing. There is nothing deeper to it. Takano most certainly does not know about past worlds at all. If she did, she'd know that her theory was complete bunk.
As for what Rika told her, she was simply interested in the fact that she predicted it successfully. The fact that she's a scientist makes her interested in what could actually be something supernatural.
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