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’s theory of quadratic residues | Statement: [Kummer theory, extends, Gauss’s theory of quadratic residues]

Target entity: Gauss’s theory of quadratic residues
Context triple: [Kummer theory, extends, Gauss’s theory of quadratic residues]

• A. Gauss’s remarkable theorem
  Gauss’s remarkable theorem is a fundamental result in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
• B. Gauss’s lemma in number theory chosen
  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.
• C. Fermat's theorem on sums of two squares
  Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
• D. Disquisitiones Arithmeticae
  Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.