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: Sperner's lemma | Statement: [Emanuel Sperner, notableConcept, Sperner's lemma]

Target entity: Sperner's lemma
Context triple: [Emanuel Sperner, notableConcept, Sperner's lemma]

• A. Sperner's lemma chosen
  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.
• B. Tucker’s lemma
  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.
• C. Borsuk–Ulam theorem
  The Borsuk–Ulam theorem is a fundamental result in algebraic topology stating that any continuous map from an n-dimensional sphere to Euclidean n-space maps some pair of antipodal points to the same point.
• D. 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.
• E. Brouwer fixed-point theorem
  The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.