I don't think 6AM E/I counts as Core programming per FCC, rather they are aired between 7AM to 10PM. [/quotre]
that changed recently. E/I can run at 6am local time and be counted
[On June 19, 2019, the FCC issued its proposed rule changes: while the basic minimum will remain intact, the earliest time allowed for E/I programming will move up an hour earlier, to 6:00 a.m. local time (which, prior to the tightening of the rules, was a common start time for children's programming on many American television stations).