We can only "prove" a negative by (allegedly) exhausting a finite space (whether physical or conceptual) and showing that the thing we are looking for isn't there.
The thing is, creation is infinite. So "proving" a negative by showing it does not exist within a finite space is almost meaningless. In general, everything exists. The negative is only part of the unbounded creation process in which a finite space is reserved where it does not exist.
This speaks to the structure of creation.
Things don't seem that way for us, because we are caught in such a finite space where in fact, many things don't exist. But even in such limited space, we can still simulate infinitely many things that don't physically exist.
Creation really only requires a universal Turing machine (or, perhaps its continuous equivalent that I haven't heard of yet.) Not that much, in the grand scheme of thing. Basically consuming nothing but space-time, pay as you go.
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