the rashidun and umayyads just took over areas that were either already riven with religious and social schism (the byzantine middle-east and north africa) or revolt (sassanid persia) and allowed the locals to govern themselves while the arabs collected taxes from them (while also giving the locals an incentive to convert to islam by instituting the jizya). they have not once built something unique, but rather cribbed from what was already there and gave it a crappier arab spin.
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