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: Gauss sums | Statement: [quadratic reciprocity law, proofMethodsInclude, Gauss sums]

Target entity: Gauss sums
Context triple: [quadratic reciprocity law, proofMethodsInclude, Gauss sums]

• A. Gauss sum chosen
  A Gauss sum is a finite exponential sum, often involving characters such as the Legendre symbol, that plays a central role in number theory and the study of quadratic and higher-order residues.
• B. Gaussian periods
  Gaussian periods are special algebraic sums of roots of unity that play a key role in number theory, particularly in constructing regular polygons like the 17-gon with straightedge and compass and in understanding cyclotomic fields.
• C. Ramanujan’s sum
  Ramanujan’s sum is a number-theoretic function introduced by Srinivasa Ramanujan, expressing certain periodic arithmetic functions as finite trigonometric sums over primitive roots of unity.
• D. Gauss’s constant
  Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
• E. Gauss’s lemma in number theory
  Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: proofMethodsInclude
Context triple: [quadratic reciprocity law, proofMethodsInclude, Gauss sums]

• A. hasProofMethod chosen
  Indicates that there exists a specific method or technique used to establish or demonstrate the validity of something (such as a statement, claim, or theorem).
• B. hasAlternativeProofMethod
  Indicates that there exists a different proof technique or approach that can be used to establish the same result or theorem.
• C. usesMethods
  Indicates that one entity employs, applies, or relies on specific methods or techniques to perform an action or achieve a result.
• D. typicalProofUses
  Indicates that a proof characteristically or commonly employs a particular method, technique, or component.
• E. includesApproach
  Indicates that one entity incorporates, utilizes, or is characterized by a particular method, strategy, or approach in relation to another entity or context.
• F. None of above.