Proof to your modern eyes. Not to the eyes of those who also called Constantinople "New Rome", and who called themselves Romans even 1000 years later.
reply"Capital of the Western World for a Cool Thousand Years" (TM)
replyMany Western polities have sought the title of the Roman Empire and the legitimacy it endows. Constantine split the empire, and Constantius II did not rule over Rome (or many other parts of the empire). Is it even reasonable to assert it was still the Roman Empire after the fracture?
replyIs it legitimate for the Eastern Roman Empire to claim the legacy? I think so, and I think they have among the best arguments for it. Conversely it is also legitimate to note the major differences between the two and the fact that discontinuities do exist.
"Constantine split the empire" is just incorrect. There were co-emperors with regional responsibilities both before and after him. They were co-emperors of one empire. If you want a firm split, 395 (death of Theodosius) is the more common date AFAIK.
replyI'm not denying that gradually, over well more than a thousand years, the empire (only surviving in the East) changed character in many ways. I am denying that a unique Eastern character sprang up (and immediately applied to Egypt) the moment that Constantinople was founded.
They actually called themselves Ῥωμαῖοι, not Romani, and not every description needs to be emic. There's nothing wrong with the label "Byzantine" except to Byzaboos.
replySo I shouldn't call them Romans, since that is an English translation of what they called themselves, and thus foreign to them.
replyBut you can call them Byzantines, an English term invented in the 19th century, because... you say so? Thank you, I have been enlightened.