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Having minimal butterflies, would this Ottoman Empire be remembered by history as being Roman? How about being recognized during its existence?:
The official name is the Roman Empire starting from Osman, with the demonym being "Roman".
Across at least the Islamic world, the term “Roman” becomes synonymous with being a subject or citizen within the Ottoman Empire.
Latin is the co-official language alongside Turkish.
Technically, Mehmed II becomes Byzantine Emperor after the Fall of Constantinople, then annexes the Ottoman Empire. This makes the Ottomans a direct continuation from Ancient Rome.
The Grand Duchy of Moscow does not declare itself as Third Rome.
The Ottoman Empire considers itself to be the Third Rome (Islamic), with First Rome being from 753 BCE-380 CE (Pagan), and Second Rome being from 380 CE-1453 CE (Christian). The Coat of arms of the Ottomans is a double-headed eagle.
The Roman Senate is restored.
Ottoman Armies are called Legions.
The majority of Islamic and Greek people in the Empire consider themselves Romans including the government, military, and academics. This is reflected in writing.
Would it take more than this?
Edit: Opps. The answer "Yes" means that it would be considered Roman. Sorry for being unclear.