I've seen this form show up a few times. In a past Japanese class, I was told that it could be used in the sense of "I haven't done X yet", as in まだ宿題をしてない.
Also, I was told that 知っている in the negative is 知らない, which makes sense, as I understand it, it's talking about "to have gained some information" vs "have not gained information", and I guess... it might be strange to say "have not gained information yet" since you might not know when you will get the information?
I'm also not asking about ている with different verbs: I know that 寝ている and 食べている have different English translations.
My question is, in regards to していない (and polite, past and contracted forms), when do we use it? What does it mean? With regards to 知る, it seems unlikely that it simply means "not in some state": it doesn't seem to be a simple negative of ている.
Here's another sentence I heard recently that made me wonder about this in particular. From SpyXFamily episode/chapter 3, we have the dialogue:
Which seems inappropriate to explain with the "not yet" idea. Maybe "not yet" is only applicable with まだ, which makes a lot of sense, but then when else is it used? In this sentence why don't we use しない or しなかった for instance?
Edit: So based on the comment from sundowner with the answer on 知る, it seems plausible that 知る is just an exception. Maybe we can leave that aside for now, I think what remains is maybe talking about my two examples: one meaning "not done X yet" and the other meaning "not doing X": is there one explanation for both? Or can we separate the usages into categories?
Edit2: Consider the post that sundowner sent. Based on intuition alone, it seems that 来ない in the last situation would mean "he's not coming", 来てない means "he's not here yet" and いない means "he's not here (right now)". Maybe this example would be helpful to explain?