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: pigeonhole principle | Statement: [Ramsey theory, basedOn, pigeonhole principle]

Target entity: pigeonhole principle
Context triple: [Ramsey theory, basedOn, pigeonhole principle]

• A. Dirichlet principle chosen
  The Dirichlet principle is a foundational concept in potential theory and the calculus of variations that asserts certain boundary value problems can be solved by finding a function minimizing an associated energy integral.
• B. 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.
• C. 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.
• D. Bertrand's postulate
  Bertrand's postulate is a theorem in number theory stating that for every integer n > 1 there is always at least one prime number strictly between n and 2n.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.