They weren't "sworn enemies," they were rival empires sharing a border. This led to frequent clashes, but there was also regular trade and diplomatic emissaries. That enables books to travel and ideas to spread.
All of your articles say the same thing, quoting again,
"It deserves to be noted that before the 12th century, the whole Byzantine output of Aristotelian commentaries dealt exclusively with the works on logic."
That's basically my point, his philosophical work was ignored. All of your sources have supported this, you even seem to be searching specifically for sources saying this now judging by that link.
What you haven't shown is any serious thought put into his philosophical work during that period, or given any other cause for his sudden resurgence besides Islamic influence. You're trying to disprove my argument that he was ignored until the Islamic works by saying "see they said Aristotle in 750, he wasn't forgotten."
Looking into this further it appears you are correct in that Al-Farabi for instance actually studied in Byzantium for 8 years according to the preface in this book:
His actual biography is unclear, much of it coming from sources hundreds of years later. What's clear is that he wrote commentaries on Aristotle's works beyond the Organon, something that is missing from Byzantine history.
As the other poster notes, he does have strong connections to Nestorian Christians of the time. They're the group that translated Aristotle from Syriac to Arabic that later led to the Latin translations bring made. And they had little to do with the Romans/Byzantines, having been condemned as heretical by the Roman church in the fifth century.
The preface is written by a translator, not a historian, and his source is another translator. Translating his works does not make him an authority on his biography. The contemporary sources are near nonexistent for his biography, and the major ones written later were contradictory.
Either way, you agree his time in Baghdad with the Nestorians came earlier, and they were far more involved in writing about Aristotle than any Byzantine known today. Maybe he did seek Greek versions of his work in Constantinople, those works were not influential in the Byzantine Empire.
I don't see how any of this is overly relevant to the discussion.
Based on your link there is a strong possibility that he studied with the Greeks. (Two sources say he did) What is mentioned no where is that Aristotle was 'forgotten' by the Greeks. In fact everywhere in those manuscripts it is assumed that the Greeks are in possession of their full philosophic heritage.
The link calls them "fabricated stories" and "legends," due to their emergence three centuries after his death. That would be like two biographies released this year on George Washington containing one sentence about how he sailed to China in his teenage years. Not a "strong possibility."
I have no idea what manuscripts you're claiming say the Greeks are in full possession of their philosophical heritage, but that is obviously false when you think about how many works have been lost over the millennia. Even being in possession of them wouldn't change that they were being ignored though, the whole "lack of commentary until the thirteenth century" bit.
Maybe, I could have phrased that better. What I meant was the assumption in the quotes listed in your link all indicate that Byzantium is where people would travel to learn Greek philosophy. Therefore even if incorrect the assumption would be that Al-Farabi would have traveled to Byzantium which was the center of Greek learning aside from a few marginal Nestorian Christians in the Caliphate at the time. There is no indication anywhere that the reverse was true.
I agree that no new commentaries were written and that Aristotle was considered a relatively minor philosopher during this time. But it's not true to state that the Caliphate was responsible for preserving his writings or that he was 'forgotten'.
However as I stated above this in my opinion is the correct way to approach Aristotle. Aristotle should be relegated to a minor role as both orthodox Christianity and later Avicennism did.
There is nothing in the biography about the Byzantine Empire at all, they're talking about the benefits of learning Greek play is the native Greek. And you're still missing the point that these were twelfth century writings, the Byzantine Empire they write of is not the one of Al-Farabi.
At no point in this tedious discussion have I said his writing was only preserved in the Caliphate, nor that he was ever "forgotten." I've made it very clear his ideas were ignored outside of Islamic philosophy, and it is contact with that philosophy that led to the it's influence in Christian philosophy. From my first post on this subject,
"I can own a book my entire life, it doesn't make me an expert on it and people I interact with won't gain an interest in it."
Good for you. Personally I find the whole "knowledge is divine insight" thing to be rubbish, but I can see why it would appeal to theistic philosophy.
This was all official dogma and part of the religious canon throughout the Byzantine empire. To say Islamic philosophy lead to the influence of Aristotle in Christianity simply isn't true. You've already admitted as much by saying that Nestorian Christianity was heavily Aristotelian. However that is not to say that later Islamic commentaries were not considered very useful. It's the unfortunate influence of Aquinas that lead to the later Aristotle fetish in the west.
All of your articles say the same thing, quoting again,
"It deserves to be noted that before the 12th century, the whole Byzantine output of Aristotelian commentaries dealt exclusively with the works on logic."
That's basically my point, his philosophical work was ignored. All of your sources have supported this, you even seem to be searching specifically for sources saying this now judging by that link.
What you haven't shown is any serious thought put into his philosophical work during that period, or given any other cause for his sudden resurgence besides Islamic influence. You're trying to disprove my argument that he was ignored until the Islamic works by saying "see they said Aristotle in 750, he wasn't forgotten."