Should I pursue a friendship with this girl who rejected me?

Got rejected by a girl earlier this past week after six dates. Said she liked me but that the feeling wasn’t persistent enough for her to see it going further especially since we would have to been long distance for the next four months.

I asked her to thing about it for a few days and she said sure and in the meantime I came around to her point of view on a lot of these things. I think are feelings are equal she just expects to feel more and I don’t have that expectation as much which is completely fair.

at the end of our second talk I brought up being friends and grabbing coffee in a few months when she’s back from college, saying I don’t like to discount connections, and she said sure, she would and that she likes to be civil with these things. I asked in a very civil way though, kind of in an afterthought/formality way and she responded in the same tone. I didn’t want to sound like a beggar.

Going forward should I attempt to pursue this friendship, maybe starting with reaching out in a few weeks? I think we’re compatible enough to be friends and have fun but the feelings aren’t so strong I can’t move on and essentially be in the friend zone. Or should I just assume she’s being polite and move on entirely, with a 100% clean break?
Should I pursue a friendship with this girl who rejected me?
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