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 for distributions | Statement: [Poincaré lemma, hasVariant, Poincaré lemma for distributions]

Target entity: Poincaré lemma for distributions
Context triple: [Poincaré lemma, hasVariant, Poincaré lemma for distributions]

• 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. 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. Cartan theorems A and B
  Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
• 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. Lectures on Cauchy’s problem in linear partial differential equations
  "Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.