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: narrow Hilbert class field | Statement: [Hilbert class field, relatedTo, narrow Hilbert class field]

Target entity: narrow Hilbert class field
Context triple: [Hilbert class field, relatedTo, narrow Hilbert class field]

• A. Hilbert class field
  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. 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.
• C. 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.
• D. Hasse norm theorem
  The Hasse norm theorem is a fundamental result in algebraic number theory that characterizes when an element of a global field is a norm from a cyclic extension by relating this property to its behavior in all completions of the field.
• E. idèle class group
  The idèle class group is a fundamental arithmetic object in number theory that encodes global information about a number field via its idèles and plays a central role in class field theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: narrow Hilbert class field
Target entity description: The narrow Hilbert class field is the maximal abelian extension of a number field that is unramified at all finite primes and corresponds to its narrow ideal class group, refining the usual Hilbert class field by also accounting for signatures at real places.

• 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. 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.
• C. 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.
• D. Hasse norm theorem
  The Hasse norm theorem is a fundamental result in algebraic number theory that characterizes when an element of a global field is a norm from a cyclic extension by relating this property to its behavior in all completions of the field.
• E. idèle class group
  The idèle class group is a fundamental arithmetic object in number theory that encodes global information about a number field via its idèles and plays a central role in class field theory.
• F. None of above.