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: class field theory | Statement: [Hilbert class field, fieldOfStudy, class field theory]

Target entity: class field theory
Context triple: [Hilbert class field, fieldOfStudy, class field theory]

• A. Noether field
  A Noether field is a type of field extension studied in invariant theory and Galois theory, arising as the fixed field of a group action on a rational function field and central to questions about rationality in Noether’s problem.
• B. Levi-Civita field
  The Levi-Civita field is a non-Archimedean ordered field of formal power series with real coefficients and well-ordered rational exponents, used to rigorously model infinitesimals and infinite quantities in analysis.
• C. global class field theory chosen
  Global class field theory is a branch of algebraic number theory that classifies finite abelian extensions of global fields (such as number fields) in terms of their arithmetic data, particularly via idele class groups and reciprocity maps.
• D. Yang–Mills theory
  Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.
• E. Schrödinger functional equation in field theory
  The Schrödinger functional equation in field theory is a generalization of the quantum-mechanical Schrödinger equation to quantum fields, describing the time evolution of wave functionals over field configurations.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.