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: Whitney embedding theorem | Statement: [Hassler Whitney, notableFor, Whitney embedding theorem]

Target entity: Whitney embedding theorem
Context triple: [Hassler Whitney, notableFor, Whitney embedding theorem]

• A. Whitney embedding theorem chosen
  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 \(\mathbb{R}^{2n}\)).
• B. Nash embedding theorem
  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.
• C. Thom transversality theorem
  The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
• D. Whitney approximation theorem
  The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
• E. Poincaré–Hopf theorem
  The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.