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 1928 paper on subsets of a finite set | Statement: [Sperner family, appearsIn, Sperner’s 1928 paper on subsets of a finite set]

Target entity: Sperner’s 1928 paper on subsets of a finite set
Context triple: [Sperner family, appearsIn, Sperner’s 1928 paper on subsets of a finite set]

• 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. Sylvester’s theorem on partitions
  Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
• C. 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.
• D. Borsuk’s partition problem
  Borsuk’s partition problem is a famous unsolved problem in geometry that asks whether every bounded set in n-dimensional Euclidean space can be divided into n+1 smaller-diameter subsets.
• E. Gale’s theorem on linear inequalities
  Gale’s theorem on linear inequalities is a fundamental result in convex geometry and linear programming that characterizes the solvability of systems of linear inequalities via an associated alternative system.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.