These results indicate that on 2012-01-02, 10 users did the born_event ("event integration"), as indicated by the first field. If the retention_type=compounded, then first will instead indicate the number of users who did event ("viewed report") on the specified date. 9 of those users did event ("viewed report") within 24 hours (the "0th" interval) of doing the born_event. Seven of those did event between 24 and 48 hours (interval 1) of the born_event. These 7 are a subset of the initial 10, but not necessarily a subset of the 9 (retention is not a funnel; see the number increase between 72 and 96 hours). And finally, 6 users did event between 48 and 72 hours (interval 2) after the born_event.
In the Mixpanel retention UI, "First time" corresponds to retention_type=birth, and "Recurring" corresponds to retention_type=compounded.
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