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: Dirichlet’s theorem on arithmetic progressions | Statement: [Multiplicative Number Theory, hasClassicResult, Dirichlet’s theorem on arithmetic progressions]

Target entity: Dirichlet’s theorem on arithmetic progressions
Context triple: [Multiplicative Number Theory, hasClassicResult, Dirichlet’s theorem on arithmetic progressions]

• A. Dirichlet's theorem on arithmetic progressions chosen
  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.
• B. Vinogradov's three-primes theorem
  Vinogradov's three-primes theorem is a landmark result in analytic number theory proving that every sufficiently large odd integer can be expressed as the sum of three prime numbers.
• C. Über die Anzahl der Primzahlen unter einer gegebenen Grösse
  Über die Anzahl der Primzahlen unter einer gegebenen Grösse is Bernhard Riemann’s seminal 1859 paper that introduced the Riemann zeta function and laid the foundations of analytic number theory, including the famous Riemann Hypothesis.
• D. Bateman–Horn conjecture
  The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
• E. Fermat's theorem on sums of two squares
  Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasClassicResult
Context triple: [Multiplicative Number Theory, hasClassicResult, Dirichlet’s theorem on arithmetic progressions]

• A. HamIs
  Indicates that one entity is identified, classified, or equated as ham in relation to another entity.
• B. hasConclusion
  Indicates that something leads to, results in, or is associated with a particular conclusion.
• C. hasComb
  Indicates that an entity possesses or is equipped with a comb.
• D. hasClassmate
  Indicates that two people attend the same class or course, making them classmates.
• E. hasCase
  Indicates that one entity is involved in, associated with, or characterized by a particular case, instance, or occurrence represented by another entity.
• F. None of above. chosen