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: Darboux theorem | Statement: [Carathéodory–Jacobi–Lie theorem, relatedTo, Darboux theorem]

Target entity: Darboux theorem
Context triple: [Carathéodory–Jacobi–Lie theorem, relatedTo, Darboux theorem]

• A. Darboux theorem chosen
  The Darboux theorem is a fundamental result in symplectic geometry stating that all symplectic manifolds are locally symplectomorphic to the standard symplectic space, implying that the symplectic form can always be put into a canonical local normal form.
• 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. 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.
• D. Cauchy–Kovalevskaya theorem
  The Cauchy–Kovalevskaya theorem is a fundamental result in partial differential equations that guarantees the existence and uniqueness of analytic solutions to certain initial value problems under appropriate analyticity conditions.
• E. Poincaré lemma
  The Poincaré lemma is a fundamental result in differential geometry and topology stating that every closed differential form on a star-shaped (or more generally, contractible) domain is locally exact.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.