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: Hales–Jewett theorem | Statement: [Ramsey theory, hasCentralConcept, Hales–Jewett theorem]

Target entity: Hales–Jewett theorem
Context triple: [Ramsey theory, hasCentralConcept, Hales–Jewett theorem]

• A. Graham–Rothschild theorem
  The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
• B. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• C. Steinhaus theorem
  The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
• D. 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.
• 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. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Hales–Jewett theorem
Triple: [Ramsey theory, hasCentralConcept, Hales–Jewett theorem]

The Hales–Jewett theorem is a fundamental result in Ramsey theory that guarantees the existence of large monochromatic combinatorial lines in high-dimensional grids under any finite coloring.

Target entity: Hales–Jewett theorem
Target entity description: The Hales–Jewett theorem is a fundamental result in Ramsey theory that guarantees the existence of large monochromatic combinatorial lines in high-dimensional grids under any finite coloring.

• A. Graham–Rothschild theorem
  The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
• B. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• C. Steinhaus theorem
  The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
• D. 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.
• 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. chosen