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: weak Lefschetz theorem | Statement: [Hard Lefschetz theorem, hasVariant, weak Lefschetz theorem]

Target entity: weak Lefschetz theorem
Context triple: [Hard Lefschetz theorem, hasVariant, weak Lefschetz theorem]

• A. Lefschetz hyperplane theorem chosen
  The Lefschetz hyperplane theorem is a fundamental result in algebraic geometry and topology that relates the topology (especially homology and homotopy groups) of a smooth projective variety to that of its hyperplane sections.
• B. Hard Lefschetz theorem
  The Hard Lefschetz theorem is a fundamental result in algebraic geometry and Hodge theory that relates the cohomology groups of a compact Kähler manifold via repeated cup product with the Kähler class, yielding powerful symmetry and duality properties.
• C. Grothendieck–Lefschetz theorem
  The Grothendieck–Lefschetz theorem is a fundamental result in algebraic geometry that extends Lefschetz-type hyperplane theorems to a broad scheme-theoretic and cohomological setting, relating the geometry and Picard groups of a variety to those of its hyperplane sections.
• D. Lefschetz
  Lefschetz is a surname most notably associated with Solomon Lefschetz, a pioneering mathematician in algebraic topology and geometry.
• 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.