Re: ""am" is before the meridian. "pm" is after the meridian"."
The meridian is, by definition, only an exact instant in time, when the sun is directly overhead. Therefore, the time that your clock displays, even the tiniest fraction of a second after the meridian, is indisputably post meridian, “pm”. Therefore, 12:00 pm (and, correspondingly, 12:00 am) works for me.
For all we know, perhaps for the barest fraction of a second digital clocks do display just 12:00 (with no suffix) just before then also displaying “pm” or “am”, has anyone ever checked? ;-)