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Proven is the wrong word. You cannot prove a theory.

Deriving a description of gravity from first principles would be more appropriate

*an empirical theory.

I can certainly prove things about, say, addition.

if you mean you can prove 2+2==4, it's actually tautology: | | + | | == | | | |

no like, "addition is closed over the integers" is something you can show to be True (for all members of an infinite set, no less -- so it's not empirical.)

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