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

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

• 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. Dolbeault cohomology classes
  Dolbeault cohomology classes are equivalence classes of differential forms on a complex manifold defined using the ∂̄-operator, encoding the manifold’s complex-analytic and geometric structure.
• 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. Poincaré duality
  Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
• E. Hodge decomposition
  Hodge decomposition is a fundamental result in differential geometry and Hodge theory that expresses differential forms on a Riemannian manifold uniquely as sums of exact, co-exact, and harmonic components.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.