A fact is something which generally agrees with the accepted body of scientific knowledge, even if it challenges specific assumptions. A non fact is something that blatantly contradicts this body of knowledge without any credible new evidence.
Mathematical facts could be said to be different, though I think they are still compatible with my definition, so they could be considered a subset. So no, I don't believe there are other kinds of facts that don't match the criteria, though of course you can subdivide the ones that do into all sorts of categories.
And while any positive statement is either a fact or a "non fact", there are plenty of things we don't know the truth of (P=NP? Gravity is quantum?), and something that today seems a fact can be a non-fact tomorrow, though this rarely happens in physics (often, some preconditions just need to be added to make the older "fact" still correct).
I'm not sure what you want me to cite. Why I believe in this definition of "fact"?
Actually, it turns out It's been me who's been wrong this whole time....I googled "fact" and came up with:
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fact
/fak(t)/
noun
1. a thing that is known or proved to be true.
2. information used as evidence or as part of a report or news article
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I was under the impression that a distinguishing factor of "fact" was Truth, now that I know that mere information is a fact, it explains a whole bunch of what confused me about this world.
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Even more interesting:
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truth
/tro͞oTH/
noun
1. the quality or state of being true.
2. that which is true or(!) in accordance with fact (see above) or reality
