And I agree; evidence for
primacy I can understand - and even support. Evidence for
supremacy, however, seems a stretch. The East was never under Papal supremacy as it is currently understood, for example.
Not in so many words, but what else can be made of it when Boniface VIII claims that the state must be subservient to the Church in all matters?
" Both, therefore, are in the power of the Church, that is to say, the spiritual and the material sword…"
“…it belongs to spiritual power to establish the terrestrial power…”
“Furthermore, we declare, we proclaim, we define that it is absolutely necessary for salvation that every human creature be subject to the Roman Pontiff.”
Change the capitalization and I agree.

But Unam Sanctam speaks to submission and subjection to the Roman Pontiff as “absolutely necessary” for salvation. What, then, of the Orthodox?
Are we forgetting the Orthodox? We must also remember that at the time this was written, the pope was pulling out all the stops, including excommunication, to force a French king to do his earthly bidding.
Now, I know that modern day Roman Catholics claim that doctrine has “developed” since the original claims of Boniface and that Unam Sanctam no longer means what it once did - but I don’t see how an honest historian can deny what it was intended to mean at the time.
Of course not. Just as we object to those who claim to use SS, but in practice use Private Interpretation.