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: Nash C∞ embedding theorem | Statement: [Nash embedding theorem, hasVersion, Nash C∞ embedding theorem]

Target entity: Nash C∞ embedding theorem
Context triple: [Nash embedding theorem, hasVersion, Nash C∞ embedding theorem]

• A. Nash embedding theorem chosen
  The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
• B. Janet–Cartan theorem
  The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
• C. Riemannian manifolds
  Riemannian manifolds are smooth manifolds equipped with an inner product on each tangent space that allows one to measure lengths, angles, and curvature in a curved geometric setting.
• D. Kakutani fixed-point theorem
  The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
• E. Annals of Mathematics
  Annals of Mathematics is a leading peer-reviewed mathematics journal renowned for publishing foundational and influential research across all areas of pure mathematics.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.