What is cultural continuity? Is France, a far more coherent nation is cultural continuous to the Gauls? Even though completely subjugated by the Romans?
Is the Islamic Republic more culturally similar to the Arab Khalifate it professes to emulate or Cyrus?
Also you brought up Sumer, how is Iran related to Sumer more than it is related to the actual Mesopotamian empires? I never heard someone claim that
I never said that. I said Susa/Sush, the beginning of Iranian civilization, is nearly as old as Sumer, by about 500 years. Historians generally consider Sumer the oldest true civilization, even if there are older settlements that didn't rise to the level of complexity rating as civilization.
Being occupied by foreign powers doesn't break cultural continuity, otherwise you'd claim the modern Greeks don't have continuity with ancient Athens, despite speaking the same language.
Continuity also doesn't mean being static. Modern Greek is not the same as classical Attic. Modern Greeks are Christian, not again, and so on.
Yes, the context however is not cultural continuity but national continuity. When someone claims Iran is bound to win because of 2500 years of empire, that seems like a joke considering the amount of foreign rule it endured.
Some hermetic cultural continuity except for language is also doubtful, Iran culture is grounded in Arabian culture no less than it is grounded in Persian culture. Hence the entire national unifying concept of Islamic Republic and heir to the Khalifates.
Regarding Susa, as far as I understand they haven't spoken an Indo-European language and Elamite is not related to Persian at all, so why do you think it shows cultural continuity?
Is the Islamic Republic more culturally similar to the Arab Khalifate it professes to emulate or Cyrus?
Also you brought up Sumer, how is Iran related to Sumer more than it is related to the actual Mesopotamian empires? I never heard someone claim that