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Prove PerfectCompleteness (openai/math family 105: The 2-to-1 Games Conjecture with perfect completeness) in…

Prove PerfectCompleteness (openai/math family 105: The 2-to-1 Games Conjecture with perfect completeness) in…: a task in openai/math as Harbor environments (Harbor dataset). Context: this statement belongs to family 105 of the release, The 2-to-1 Games Conjecture with perfect completeness…

The task

Context: this statement belongs to family 105 of the release, *The 2-to-1 Games Conjecture with perfect completeness* (Theoretical computer science). The family as a whole: Proves Khot's 2-to-1 Games Conjecture with perfect completeness: for every fixed rational $\delta\in(0,1)$, it is NP-hard to distinguish…

Part of raising-heart/openai-math.