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: Kronecker–Weber theorem over the rationals | Statement: [Artin reciprocity law, implies, Kronecker–Weber theorem over the rationals]

Target entity: Kronecker–Weber theorem over the rationals
Context triple: [Artin reciprocity law, implies, Kronecker–Weber theorem over the rationals]

• A. Kronecker–Weber theorem chosen
  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.
• 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. absolute Galois group of the rational numbers
  The absolute Galois group of the rational numbers is the profinite group of all field automorphisms of an algebraic closure of Q that fix Q, encoding the full arithmetic and algebraic extension structure of the rational numbers.
• D. 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.
• E. Hilbert’s irreducibility theorem
  Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.