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–Levin theorem | Statement: [NP-hardness, historicalWork, Cook–Levin theorem]

Target entity: Cook–Levin theorem
Context triple: [NP-hardness, historicalWork, Cook–Levin 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. Papadimitriou–Yannakakis theorem
  The Papadimitriou–Yannakakis theorem is a fundamental result in computational complexity theory that characterizes the complexity of certain optimization and approximation problems, particularly in relation to classes like NP and the theory of approximation algorithms.
• C. 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.
• D. 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.
• E. P versus NP problem
  The P versus NP problem is a central unsolved question in theoretical computer science that asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: historicalWork
Context triple: [NP-hardness, historicalWork, Cook–Levin theorem]

• A. historicalReference
  Indicates that one entity refers to, cites, or alludes to another entity from an earlier time or historical context.
• B. historicalCategory
  Indicates that an entity is classified within a particular historical grouping, period, or type based on its time-related characteristics or context.
• C. historicalProject
  Indicates a relationship where an entity is or was involved in, associated with, or characterized by a project of historical significance or from a past period.
• D. historicalMedium
  Indicates that an entity was conveyed, recorded, or expressed through a particular medium or format in its original historical context.
• E. historicalMaterial
  Indicates that something serves as a source or document providing information or evidence about past events or conditions.
• F. None of above. chosen