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Could most of Europe have been united into a single state or empire by the end of the High Middle Ages? (POD can be any time period, even in ancient times).
By most of Europe, I mean about 70% of the continent's area. Tributaries, client kingdoms, and vassal states count as part of the empire's area, even if not directly administered.
Bonus points: Center the empire around the European Plain, instead of Rome or Constantinople.