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Yes. after defaults to five minutes before the call, so a code that landed just before you asked still counts. Pass the time you requested the code as after and anything older is ignored. On timed_out, call again with the same after.

Thanks. Empty buckets are returned, not skipped. Every UTC hour (or day) from the floored start through the bucket that contains the instant before end is in the series with zero counts, so you can chart it without filling gaps. The end instant is exclusive.