Again, I ask you some sources about this. I pointed you to contemporary sources about these titles (and almost all can be found translated in English, if you have trouble with Latin).
If you're right, it shouldn't be too hard to find contemporary documents or sources (good luck going trough Carolingian coinage, tough) supporting your case, isn't?
And it would be more convincing than "you're deluded" or "you're nipticking" reactions.
Meanwhile : I tried to explain you the difference between the Carolingian title style, Ottonian style and Byzantine style already.
Carolingians didn't claimed Romania, but an imperium over Christians (which passed trough the pontifical support). It's made particularly obvious with Alcuin's stance over "The Empire of Christians".
Similarly Ottonians claimed so, while also claiming a Roman title with Otto II. Byzantines were so pissed at this they readily agreed to marry twice with Ottonians.
And while Byzantine claimed imprium over Romans, it was less Rome they claimed (at least not after the VIIIth century) than upon Roman peoples.
The use, including by Latins, of "Empire/Emperor of Romania" to name Byzantium is simply too well attested to be ignored.
Rome was important for the western imperialship definition, and less as a city than for the Pontifical legitimisation, at the point Carolingians never went the effort to name themselves "Roman Emperors" or "Emperors of the Romans" or "Emperors of Rome".
As for Byzantines, they didn't cared about the city, but the political implication of the title, as for as far they were concerned, the only Romans were them (Roman as a political identity still existed in the western part after the fall of WRE, but went quickly absorbated by Barbarian political identities, which were contradictory with roman citizenship).
Not that you didn't have struggles on the imperial title, but it was about the imperium rather than the Roman part (they had knee-jerk reactions on "unlawful" use of basileus, for exemple). It was enough for that Carolingians claimed the imperium only for that Emperors in Constantinople were annoyed (never at the point to make a diplomatic scandal about it, tough. They often just ignored the claim or made fun of it).
Now if you don't mind, as I'm a bit tired of running circles there, I'll stand with that. Anyone interested can dig in contemporary sources about styles and titles themselves to make its own opinion.
Mostly, yes, while you had a geographical distinction.
Basically, Latin and Greek were both Roman administrative, chancery and political languages. Something that no other language in the Empire was.
Latin was dominant in the western part (with some exceptions), while still with an important hellenistic influence on upper classes; while Greek was dominant (by political choice) over the other languages used in the eastern parts.
Well, don't tell anyone, but Biden and I are two different and unrelated persons. Some even say we may think idependently from each other.
For exemple, I don't think Rome had "one" heart, but multiple depending on which matter we're talking about. Danubian regions were a military focal point (and therfore, growingly political), for exemple.
Now, yes. The Eastern part of the empire always was a really important focus of the Empire, would it be for a more important role into production and fiscal entries. And it never ceased to have a growing importance after the IInd century.
You can easily go for 500,000 or 600,000 for the IInd century. More importantly, the population doesn't seem to have significantly lowered before the Arab conquests, while Rome's population declined.
Arguably, I should've precised : was the demographical equal of Rome in the Late Empire. Point taken and correction made.
I think we can agree with Alexandria being second only behind Rome in matter of population.
(While being more active, economically-wise).
Egypt, nevertheless, with an important population stuck into a fairly reduced inhabitable land, certainly had a more important density. At least according
these estimations.
That's for the
Italian numbers, not the whole of Romania.
We're talking 10 millions citizens for the late Republic, 15 millions for the Ist Century, a number that grew continuously with whole peoples and cities being granted citizenship (while
deductio went extinct). For exemple, whole of Hispania obtained Roman citizenship under Vespasian.
Not only roman citizenship was widespread enough before the Edict of Caracalla (again, the exemple of the whole Mauretania or Hispania recieving citizenship), but once again arguing so is irrelevant : by 212 almost everyone was made citizen within the Empire, including *gasp* Romans Greeks.
Seriously : would it be only because History didn't jumped overnight from Ist Century to VIIIth century, one should take a look at what happened meanwhile.