DATE('T') returns apparently the same number as time('T') without mentioning that in the reference.

Say date(T,20200427,S) uses today's time 00:00:00

Regina does the same and talks about it a little more:

[T]
(time_t) Returns the current UTC date/time in UNIX time_t format. time_t is the number of seconds since January 1st 1970. It always represents the UTC date/time, so any conversion from another date format (which is always assumed to be local time) will result in a time_t value offset by time zone. (Regina Extension)

( I don't undetstand the latter part of this explanation :-( )

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