How we cite our quotes: (Article.Sentence)
Quote #4
There shall be a firm and perpetual peace between his Brittanic Majesty and the said states, and between the subjects of the one and the citizens of the other, wherefore all hostilities both by sea and land shall from henceforth cease. (7.1)
Listen to that language: "between the subjects of one and the citizens of the other." This is acknowledging two different powers and even the differing relationships the government has with their people. To a king, these are subjects. To a republic, these are citizens. There's a difference and in the language of the treaty, that's highlighted.
Quote #5
In case it should so happen that any place or territory belonging to Great Britain or to the United States should have been conquered by the arms of either from the other before the arrival of the said Provisional Articles in America, it is agreed that the same shall be restored without difficulty and without requiring any compensation. (9.1)
You don't return territory to an illegitimate state. Because of how slow news traveled back then, provisions like this were often necessary. The idea that territory could be returned to the United States fairly marked it as its own thing.