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by repsilat 3866 days ago
> If P=NP is independent, then we already know that a complete search for a polynomial algorithm for 3SAT will fail

A search for a provably polynomial algorithm will fail, but that doesn't mean that an unprovably polynomial time algorithm couldn't exist. We might come up with strong arguments for why a particular algorithm would be polynomial in practice. Still, I'd say "independent but false" is more likely than "independent but true."