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: Szemerédi's theorem, which uses combinatorial density conditions | Statement: [Erdős–Turán conjecture, contrastWith, Szemerédi's theorem, which uses combinatorial density conditions]

Target entity: Szemerédi's theorem, which uses combinatorial density conditions
Context triple: [Erdős–Turán conjecture, contrastWith, Szemerédi's theorem, which uses combinatorial density conditions]

• A. Szemerédi's theorem chosen
  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.
• 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. Hales–Jewett theorem
  The Hales–Jewett theorem is a fundamental result in Ramsey theory that guarantees the existence of large monochromatic combinatorial lines in high-dimensional grids under any finite coloring.
• D. 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.
• E. Graham–Rothschild theorem
  The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.