Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Cook’s theorem | Statement: [P versus NP problem, formalizedIn, Cook’s theorem]

Target entity: Cook’s theorem
Context triple: [P versus NP problem, formalizedIn, Cook’s theorem]

• A. Cook–Levin theorem chosen
  The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
• B. PCP theorem
  The PCP theorem is a fundamental result in computational complexity theory stating that every problem in NP has probabilistically checkable proofs that can be verified by examining only a constant number of bits, with major implications for the hardness of approximation.
• C. Böhm–Jacopini theorem
  The Böhm–Jacopini theorem is a foundational result in computer science stating that any computer program can be written using only sequence, selection, and iteration constructs, without requiring goto statements.
• D. Valiant–Vazirani theorem
  The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
• E. Entscheidungsproblem
  The Entscheidungsproblem is a foundational decision problem in mathematical logic that asks whether there exists a general algorithm to determine the truth or falsity of any given first-order logical statement.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.