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: Ax–Katz theorem | Statement: [Chevalley–Warning theorem, relatedTo, Ax–Katz theorem]

Target entity: Ax–Katz theorem
Context triple: [Chevalley–Warning theorem, relatedTo, Ax–Katz theorem]

• A. 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.
• 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. 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.
• D. Erdős–Turán inequality
  The Erdős–Turán inequality is a fundamental result in analytic number theory that provides quantitative bounds on the discrepancy of sequences by relating uniform distribution to exponential sums.
• E. Gowers inverse theorem in additive combinatorics
  The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Ax–Katz theorem
Target entity description: The Ax–Katz theorem is a result in number theory that gives precise divisibility bounds for the number of solutions to polynomial equations over finite fields, strengthening and refining the Chevalley–Warning theorem.

• A. 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.
• 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. 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.
• D. Erdős–Turán inequality
  The Erdős–Turán inequality is a fundamental result in analytic number theory that provides quantitative bounds on the discrepancy of sequences by relating uniform distribution to exponential sums.
• E. Gowers inverse theorem in additive combinatorics
  The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
• F. None of above. chosen