I disagree NOT , is not about extant , Not is about what you don't have . The opposite of not , HAVE .
That strikes me conceptually as the same thing as existentiality/extant. He is not sober. He has inebriation. He is sober. He hasn't inebriation. He has the right to vote. He is enfranchised. He hasn't the right to vote. He is disenfranchised. Because they do, I'm now of a mind that you and I are both mistaken. Thinking a bit more about it, and maintaining as before that the opposite of "not" needs to be an adverb, I retract my earlier answer and instead go with the collection of words that one way or another convey the meaning of "truly," "actually," "absolutely," "utterly," "indeed," etc. Considering the examples above that seems to work. He is not sober. He is truly sober. He hasn't the right to vote. He indeed has the right to vote. Earth actually has a satellite. Earth does not have a satellite. The loser was not defeated. The loser was utterly defeated. Looking at the examples applicable to my revised answer, I'm convinced that I've found the correct line of thought and conclusion about what is the linguistic opposite of "not." Indeed, seeing the clear redundancy of including "truly," "indeed," "utterly," and "actually" in the sentences above, one sees instantly why we don't typically use words that are the opposite of "not," save for in instances in which an author feels obliged to emphasize the "oppositeness of not," as it were, for no different state of being, having, etc. is identified or described by including words that have meanings opposite to that of "not."
I'd say "is". If you say something is not there, removing the "not" leaves only "is" and therefore affirms the statement.
That may not apply, and so does not suffice, will not always work, and not uncommonly would not even suggest itself.
