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: Cartan theorem B | Statement: [Cartan theorems A and B, hasPart, Cartan theorem B]

Target entity: Cartan theorem B
Context triple: [Cartan theorems A and B, hasPart, Cartan theorem B]

• A. Cartan theorems A and B chosen
  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.
• 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. 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.
• D. Oka–Grauert principle
  The Oka–Grauert principle is a fundamental result in complex geometry asserting that, for certain complex manifolds, topological and holomorphic classification problems coincide, allowing topological data to determine holomorphic structures.
• E. Oka–Weil theorem
  The Oka–Weil theorem is a fundamental result in several complex variables that extends Runge’s approximation theorem by characterizing when holomorphic functions on certain compact sets in complex manifolds can be uniformly approximated by global holomorphic functions.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.