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: Green–Tao theorem | Statement: [Ben Green, notableTheorem, Green–Tao theorem]

Target entity: Green–Tao theorem
Context triple: [Ben Green, notableTheorem, Green–Tao theorem]

• A. Green–Tao theorem chosen
  The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
• B. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• C. Dirichlet's theorem on arithmetic progressions
  Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
• D. Erdős–Turán conjecture
  The Erdős–Turán conjecture is an unsolved problem in additive number theory asserting that any subset of the positive integers with divergent sum of reciprocals must contain arbitrarily long arithmetic progressions.
• E. Roth theorem
  Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: notableTheorem
Context triple: [Ben Green, notableTheorem, Green–Tao theorem]

• A. hasTheorem
  Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
• B. notableTheorist
  Indicates that the subject is recognized as a significant or influential theorist in relation to the object or specified field.
• C. hasTheoremNamedAfter chosen
  Indicates that a theorem is named in honor of or after a particular person or entity.
• D. notableFor
  Indicates that an entity is especially recognized or distinguished for a particular quality, achievement, characteristic, or role.
• E. notableProposition
  Indicates that a subject is associated with a proposition, statement, or claim that is considered notable or significant in some context.
• F. None of above.