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: Hardy–Littlewood circle method | Statement: [Hardy–Ramanujan asymptotic formula, methodIntroducedWith, Hardy–Littlewood circle method]

Target entity: Hardy–Littlewood circle method
Context triple: [Hardy–Ramanujan asymptotic formula, methodIntroducedWith, Hardy–Littlewood circle method]

• A. Hardy–Littlewood circle method chosen
  The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
• B. Hardy–Ramanujan asymptotic formula
  The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
• C. Dirichlet hyperbola method
  The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
• D. Selberg sieve
  The Selberg sieve is a powerful analytic number theory method developed by Atle Selberg for estimating the size of sets of integers filtered by divisibility conditions, particularly in the study of prime numbers.
• E. Hardy–Littlewood conjectures
  The Hardy–Littlewood conjectures are a collection of influential unproven hypotheses in analytic number theory that generalize the prime number theorem to describe the distribution of prime numbers and prime constellations.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: methodIntroducedWith
Context triple: [Hardy–Ramanujan asymptotic formula, methodIntroducedWith, Hardy–Littlewood circle method]

• A. introducedWithVersion
  Indicates that something first became available or was added starting from a specific version.
• B. messageIntroducedWith
  Indicates that one message is presented or initiated by means of another message or introductory content.
• C. introducedAfter
  Indicates that one entity was introduced at a later time or stage than another entity.
• D. introducedInSystem
  Indicates that an entity was first added, implemented, or made available within a particular system.
• E. formatIntroduced
  Indicates that a particular format was first introduced or made available at a specific time or in a specific context.
• F. None of above. chosen