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: Janet–Cartan theorem | Statement: [Maurice Janet, hasNotableTheoremNamedAfter, Janet–Cartan theorem]

Target entity: Janet–Cartan theorem
Context triple: [Maurice Janet, hasNotableTheoremNamedAfter, Janet–Cartan theorem]

• A. Janet–Cartan theorem chosen
  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.
• B. Carathéodory–Jacobi–Lie theorem
  The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
• C. 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.
• D. Gauss–Bonnet theorem (early form)
  The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
• E. 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 \(\mathbb{R}^{2n}\)).
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasNotableTheoremNamedAfter
Context triple: [Maurice Janet, hasNotableTheoremNamedAfter, Janet–Cartan theorem]

• A. hasAwardNamedAfter
  Indicates that an entity has an award that is named in honor of another entity.
• B. hasNotableHonoree
  Indicates that an entity is notably dedicated to, named after, or honors a particular person or group.
• C. notableScientist
  Indicates that the subject is a scientist who is widely recognized for significant contributions or impact in their field.
• D. hasAsteroidNamedAfter
  Indicates that an asteroid has been officially named in honor of a particular entity.
• E. historicallyFormulatedBy chosen
  Indicates that something (such as an idea, theory, or document) was originally developed, articulated, or formally established by a particular agent or group in the past.
• F. None of above.