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The polynomial hierarchy PH, the union of the levels Sigma_k^p, Pi_k^p, and Delta_k^p built from NP and coNP with polynomial-time oracles. Claims about its levels, its collapse (to P, to a level, or conditionally), and its relations to classes such as PSPACE belong here; general complexity-class theory without PH as its subject stays under Computational complexity theory.

If P equals NP, the polynomial hierarchy collapses to P.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →P versus NP problem Computational complexity theoryimportance · settledImportance 0.12, from 0 to 1 · settled: uncontested, so low even when much depends on it. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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