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 reciprocity law | Statement: [Hasse norm theorem, relatedTo, Hilbert reciprocity law]

Target entity: Hilbert reciprocity law
Context triple: [Hasse norm theorem, relatedTo, Hilbert reciprocity law]

• A. Artin reciprocity law
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• B. 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.
• C. Chebotarev density theorem
  The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
• D. Hilbert symbol
  The Hilbert symbol is a local arithmetic invariant in number theory that encodes whether a quadratic form represents zero over a given local field, playing a central role in local class field theory and reciprocity laws.
• E. quadratic reciprocity law
  The quadratic reciprocity law is a fundamental theorem in number theory that characterizes when a quadratic equation modulo one odd prime has solutions in terms of solvability modulo another, revealing a deep symmetry between primes.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Hilbert reciprocity law
Triple: [Hasse norm theorem, relatedTo, Hilbert reciprocity law]

The Hilbert reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing how local norm residue symbols at all places of a number field multiply to 1, linking local and global arithmetic properties.

Target entity: Hilbert reciprocity law
Target entity description: The Hilbert reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing how local norm residue symbols at all places of a number field multiply to 1, linking local and global arithmetic properties.

• A. Artin reciprocity law
  The Artin reciprocity law is a fundamental theorem in class field theory that generalizes quadratic reciprocity by describing abelian extensions of number fields in terms of characters of their idele class groups.
• B. 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.
• C. Chebotarev density theorem
  The Chebotarev density theorem is a fundamental result in algebraic number theory that generalizes the prime number theorem to describe how often primes in a number field have a given Frobenius conjugacy class in its Galois group.
• D. Hilbert symbol chosen
  The Hilbert symbol is a local arithmetic invariant in number theory that encodes whether a quadratic form represents zero over a given local field, playing a central role in local class field theory and reciprocity laws.
• E. quadratic reciprocity law
  The quadratic reciprocity law is a fundamental theorem in number theory that characterizes when a quadratic equation modulo one odd prime has solutions in terms of solvability modulo another, revealing a deep symmetry between primes.
• F. None of above.