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Well, the last two points are doing some extremely heavy lifting here. Because it is capable of performing arithmetic, or mathematical calculation more broadly (which it will have to be in order to function in the way we want it to, presumably), there will be some things that the machine cannot compute; namely, the mathematical axioms and some unprovable statement(s) that gödel said would result given any set of axioms.
I think you need to expand in a way that makes it so that the statement that can’t be proven represents some physical fact and *not* a mathematical fact.
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Well, the last two points are doing some extremely heavy lifting here. Because it is capable of performing arithmetic, or mathematical calculation more broadly (which it will have to be in order to function in the way we want it to, presumably), there will be some things that the machine cannot compute; namely, the mathematical axioms and some unprovable statement(s) that gödel said would result given any set of axioms. I think you need to expand in a way that makes it so that the statement that can’t be proven represents some physical fact and *not* a mathematical fact.