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: de Rham theorem | Statement: [Poincaré lemma, usedInProofOf, de Rham theorem]

Target entity: de Rham theorem
Context triple: [Poincaré lemma, usedInProofOf, de Rham theorem]

• A. de Rham cohomology chosen
  de Rham cohomology is a cohomology theory for smooth manifolds that uses differential forms to capture their global topological and geometric properties.
• B. Mayer–Vietoris sequence in de Rham cohomology
  The Mayer–Vietoris sequence in de Rham cohomology is a long exact sequence that computes the de Rham cohomology of a manifold by relating it to the cohomology of an open cover and their intersection.
• C. Chern–Weil theory
  Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
• 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.