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 embedding theorems | Statement: [Janet–Cartan theorem, relatedTo, Nash embedding theorems]

Target entity: Nash embedding theorems
Context triple: [Janet–Cartan theorem, relatedTo, Nash embedding theorems]

• 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. Whitney embedding theorem
  The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
• C. 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.
• D. 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.
• 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.