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 Disquisitiones Arithmeticae | Statement: [Book III (Disquisitiones Arithmeticae), isComponentOf, Gauss’s Disquisitiones Arithmeticae]

Target entity: Gauss’s Disquisitiones Arithmeticae
Context triple: [Book III (Disquisitiones Arithmeticae), isComponentOf, Gauss’s Disquisitiones Arithmeticae]

• A. Disquisitiones Arithmeticae chosen
  Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
• B. 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.
• C. 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.
• D. Treatise on Demonstration of Problems of Algebra
  Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
• E. Three Pearls of Number Theory
  Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.