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: Tucker’s lemma | Statement: [Ky Fan’s lemma, generalizes, Tucker’s lemma]

Target entity: Tucker’s lemma
Context triple: [Ky Fan’s lemma, generalizes, Tucker’s lemma]

• A. Tucker’s lemma chosen
  Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
• B. Sperner's lemma
  Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
• C. Knaster–Kuratowski–Mazurkiewicz lemma
  The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
• D. Scarf’s lemma
  Scarf’s lemma is a fundamental result in combinatorial topology and game theory that guarantees the existence of approximate solutions to certain systems, underpinning proofs of equilibrium existence in economics and related fields.
• E. Ky Fan’s lemma
  Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.