P?=NP Troll Edition!
P=NP but the proof is not constructive
P=NP but the algorithm is not physically realisable
P=NP but requires self-modifying code that is not intelligible
P!=NP but proof too large to be practical
Independent of current axioms so unprovable
P=NP, but the only proof is an O(n^999) algorithm for SAT generated by an AI and nobody understands the AI's explanation for how it works or why it says no algorithm with better upper bound exists.
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