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: Hopf degree theorem | Statement: [Heinz Hopf, notableWork, Hopf degree theorem]

Target entity: Hopf degree theorem
Context triple: [Heinz Hopf, notableWork, Hopf degree theorem]

• A. Hopf invariant chosen
  The Hopf invariant is a topological integer-valued invariant that classifies certain continuous maps between spheres, playing a central role in homotopy theory and the study of higher-dimensional linking.
• B. Hirzebruch signature theorem
  The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
• C. Hopf conjecture (on Euler characteristic and curvature)
  The Hopf conjecture on Euler characteristic and curvature is an open problem in differential geometry proposing a deep link between the sign of a manifold’s Euler characteristic and the sign of its sectional curvature, especially for even-dimensional manifolds with positive or negative curvature.
• D. 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.
• E. h-cobordism theorem
  The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.