I disagree. The legitimacy of any Roman regime did not derive from the Emperor, but from the Senate and other such political institutions. That is where the continuity comes in.
Even if that was the case (the Senate was just a figurehead and progressively lost even more power and importance with the passing years), overthrowing an emperor is still a great overhaul that counts as a break.
What is the specific institution, actual and concrete, (or multiple ones) that tied every dynasty together?
Principally, the scholar bureaucracy that operated under the idea of the Mandate of Heaven.
There was no break, there were territories lost, and reconquered.
By this logic, the Three Kingdoms is no break of the Han regime either since the regime left by the Han actually kept operating under Cao Pi as the state of Cao Wei, with the different territories that broke into the Three Kingdoms then reunified under the Sui-Wei. Fact is, in the crisis of the 3rd century, the emergence of multiple emperors outside of Rome and the deposing of emperors in Rome is as much a break as the deposition of the last Eastern Han emperor that led to the Three Kingdoms.
Dynasties barely mattered in Rome, other than as a convenience. People preferred to have a son succeed a father, simply because it made things easy to predict, but the amalgamation of offices that comprised the Imperial position were not tied into any dynastic claim.
You're partially right (the same thing can be said of Chinese dynasties after all), I'm merely adding dynastic claims to the heap of why there was political break in the empire in the third century crisis or with the Tetrarchy at the very least. Complete overhauling of emperors, officials and changes in the governing system are breaks from the prior regime.
Incorrect. There was as much political continuity as any other state that moved its capital. Like Spain moving from Toledo to Madrid. Or any number of Chinese dynasties that moved their capitals.
Not in this case when Constantine completely overhauled the entire Tetrarchy system which is further signified by changing the capital from Rome to Byzantium. And I would agree that changes of capitals are breaks in political continuity anyway.
There was no 'traditional line of rulers of Byzantium.' The Heraclians had been in power for awhile, and the Justinianic dynasty had preceded them, and so on and so forth. You haven't given me anything that makes Justinian II special, particularly when compared to other last emperors in a given dynasty. Why Justinian II and not Maurice, or Nero, or Domitian, or Commodus, or Julian, or anyone else?
You shoot yourself in the foot when you agree that there had been at least two prior dynasties. Moreover, Justinian II's is especial not only because there were three emperors in quick succession (Justinian, Leontios and Tiberios) but because his final overthrow by Philippikos Bardanes led to the further deposition of the Christian Patriarch (at a time when the Church had pretty much completely replaced the Senate) and the establishment of a heresy as the official religion of the empire (monotheletism). No different than the deposition of Xian of Han by Cao Pi that led to the Three Kingdoms period, or the prior deposition of Qin Shi Huang by Liu Bang.
That would depend on the circumstances, possibly (ignoring that murky area that was Wang Mang's dynasty).
For the record I would accept Wang Mang's overthrow of the Western Han as a break, as you so strongly seem to be inclined to accept.
Nope. The Empire persisted, with the political capital remaining free of foreign control. Losing the periphery does not break continuity. Alaric sacked a prestigious city, he didn't sack the seat of political power in the West, let alone the East.
Again, by this logic, the Qin empire continued with the Han which continued with Cao Wei which continued with the Sui-Wei, and so on, if you're going to say that all those examples are just loss of territory when we also see complete unrecognition and even deposition. And if Alaric's taking of Rome doesn't count, there's still Odoacer's conquest in 476 which is traditionally marked as the fall of the Western Roman Empire.
Also, periphery? The Arabs took all of North Africa, including Egypt, and the Eastern Mediterranean, which composed the majority of the Roman Empire. The Palmyrenes beforehand had taken Egypt and as far as southern Asia Minor. By your logic, the rival states of Cao Wei also only took the "periphery".
Incorrect. Nobody claiming the title of Roman Emperor every acknowledged the legitimacy of any other Roman Emperor, as an independent ruler. The only times other Emperors were acknowledged as Emperors were co-Emperors, who were governing the Empire in conjunction with each other. Thats no more a break in continuity than the Roman consuls were.
If anything the non-recognition between rival emperorst only reinforces my argument that there was a break contrary to your argument that Rome lasts until the Fourth Crusade.
Except for the Three Kingdoms, the Northern and Southern dynasties, and the 5 Dynasties and 10 Kingdoms. And, though Chinese history is not my area of expertise, it is my understanding that the ushering in of a new dynasty claiming the Mandate of Heaven was seen as a slightly bigger deal than a given Roman general winning a civil war and being ratified as Emperor by the Senate.
If anything, the idea of the Mandate of Heaven provided a myth of unstopped political continuity for the Central State (Zhongguo) that ruled All Under Heaven (Tianxia). You can see this in the Shujing where, for instance, the overthrowing of the Shang by the Zhou is not seen as a break, just a change of one immoral dynasty to a moral one; basically, it's seen in the same way as the assassination of Caligula which is not a political break according to you.