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: Poincaré lemma | Statement: [de Rham cohomology, relatedConcept, Poincaré lemma]

Target entity: Poincaré lemma
Context triple: [de Rham cohomology, relatedConcept, Poincaré lemma]

• A. Poincaré lemma chosen
  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.
• B. Morse lemma
  Morse lemma is a fundamental result in differential topology that locally characterizes a non-degenerate critical point of a smooth function as being equivalent, via a coordinate change, to a quadratic form.
• C. 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.
• D. Darboux theorem
  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.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.