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While I don't necessarily think there is (or should be) a TOE, Omega does not serve as proof for the non-existence of a TOE.

This is simply because a TOE is not at all required to allow deriving Omega from it.

Omega is defined in domain terms, broadly taking from computer science. We can come up with other mathematically rigorous definitions of numbers standing for philosophical issues that cannot be computed. These are applications. Mathematics has no interest in that.

- IR