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Hm, are you talking about the time dilation feature, or are you talking about showing projected rating in the ladder (and using it for sorting/matchmaking)?
I mean you said a rating period lasts 15 battles or two days. Seeing as how not every player will take the same amount of time to have 15 battles, I assume that means that each player has their own rating period.
Oh yeah, that's time dilation. I made a post about it somewhere. Yes, that's how it works, I got the idea when I got really anomalous results after 15 battles in the same rating period (stuff like losing points for winning battles), because Glicko2 just isn't designed for that many.