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: Euler characteristic | Statement: [Morse theory, keyConcept, Euler characteristic]

Target entity: Euler characteristic
Context triple: [Morse theory, keyConcept, Euler characteristic]

• A. Euler–Poincaré characteristic formula chosen
  The Euler–Poincaré characteristic formula is a fundamental relation in topology and algebraic geometry that expresses a space’s Euler characteristic in terms of alternating sums of dimensions of its cohomology groups.
• B. Betti numbers
  Betti numbers are topological invariants that count the number of independent cycles or holes in each dimension of a topological space, reflecting its underlying shape and structure.
• C. Lefschetz number
  The Lefschetz number is a topological invariant, computed from the traces of induced maps on homology, that predicts the existence and number of fixed points of a continuous self-map on a topological space.
• 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. Euler class
  The Euler class is a topological characteristic class associated with oriented real vector bundles, capturing obstruction information such as the existence of nowhere-vanishing sections.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.