The orthodoxy is that the two most common forms of time stamps are:

(1) Unambiguous: a time in the past that is represented by the number of seconds since the epoch, Jan 1 1970. When coupled with a location/jurisdiction, they can be converted into a wall-clock time like “1:23pm 04 May 2006 Europe/Paris.”

(2) Ambiguous (but semantically meaningful): a time in the future that would be shown on a clock at the location of the event.

The logging of IP addresses would use the former.

The upcoming trial date for illegal torrenting would use the latter.

Let's go a step further and use TAI to avoid leap seconds while we're at it.