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: Hilbert class field | Statement: [Artin reciprocity law, relatedTo, Hilbert class field]

Target entity: Hilbert class field
Context triple: [Artin reciprocity law, relatedTo, Hilbert class field]

• A. Hilbert class field chosen
  The Hilbert class field of a number field is its maximal unramified abelian extension, central in class field theory as it corresponds to the field’s ideal class group.
• B. Hilbert’s twelfth problem
  Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
• C. Furtwängler’s theorem in class field theory
  Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
• D. Kronecker–Weber theorem
  The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
• E. Hilbert class polynomial
  The Hilbert class polynomial is a key object in algebraic number theory whose roots generate the Hilbert class field of an imaginary quadratic field and play a central role in complex multiplication and explicit class field theory.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.