> An empire is an ideology which emanates from a seat of power.

Yes, not from a fixed physical location. If the empire fell when rome ceased to be "the seat of power" it was no longer the Roman empire by ~300 AD was it? Diocletian was larping...

The Roman empire continiously changed and evolved. The empire in ~300 AD wouldn't have made any sense to Romans from 100 BC (and probably a lot more sense to the Romans from 1000 AD)