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: Roth's theorem on three-term arithmetic progressions | Statement: [Klaus Roth, notableWork, Roth's theorem on three-term arithmetic progressions]

Target entity: Roth's theorem on three-term arithmetic progressions
Context triple: [Klaus Roth, notableWork, Roth's theorem on three-term arithmetic progressions]

• A. Roth theorem chosen
  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.
• B. Green–Tao theorem
  The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
• C. Erdős discrepancy problem
  The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
• D. 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.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.