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: On embeddings of spheres | Statement: [Barry Mazur, doctoralThesis, On embeddings of spheres]

Target entity: On embeddings of spheres
Context triple: [Barry Mazur, doctoralThesis, On embeddings of spheres]

• A. Smale–Hirsch immersion theorem
  The Smale–Hirsch immersion theorem is a fundamental result in differential topology that classifies immersions of manifolds up to regular homotopy in terms of bundle monomorphisms between their tangent bundles.
• 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. 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 \(\mathbb{R}^{2n}\)).
• D. Thom cobordism theory
  Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
• E. The geometry of four-manifolds
  The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: On embeddings of spheres
Target entity description: "On embeddings of spheres" is Barry Mazur's influential doctoral thesis in topology, focusing on the study of how spheres can be embedded in higher-dimensional manifolds.

• A. Smale–Hirsch immersion theorem
  The Smale–Hirsch immersion theorem is a fundamental result in differential topology that classifies immersions of manifolds up to regular homotopy in terms of bundle monomorphisms between their tangent bundles.
• 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. 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 \(\mathbb{R}^{2n}\)).
• D. Thom cobordism theory
  Thom cobordism theory is a foundational branch of algebraic topology developed by René Thom that classifies manifolds up to cobordism using homotopy-theoretic and characteristic class methods.
• E. The geometry of four-manifolds
  The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
• F. None of above. chosen