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 theorem | Statement: [Sperner family, centralResult, Sperner theorem]

Target entity: Sperner theorem
Context triple: [Sperner family, centralResult, Sperner theorem]

• A. Sperner family
  A Sperner family is a collection of subsets of a finite set in which no subset is contained within another, central in extremal set theory and combinatorics.
• B. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• C. Dilworth theorem
  Dilworth's theorem is a fundamental result in order theory that relates the size of the largest antichain in a finite partially ordered set to the minimum number of chains needed to cover the set.
• D. 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.
• E. Erdős–Szekeres theorem
  The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Sperner theorem
Target entity description: Sperner's theorem is a fundamental result in extremal set theory that determines the maximum size of a family of subsets of an n-element set in which no set is contained in another.

• A. Sperner family chosen
  A Sperner family is a collection of subsets of a finite set in which no subset is contained within another, central in extremal set theory and combinatorics.
• B. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• C. Dilworth theorem
  Dilworth's theorem is a fundamental result in order theory that relates the size of the largest antichain in a finite partially ordered set to the minimum number of chains needed to cover the set.
• D. 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.
• E. Erdős–Szekeres theorem
  The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
• F. None of above.