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: Tverberg’s theorem | Statement: [Helly’s theorem, relatedTo, Tverberg’s theorem]

Target entity: Tverberg’s theorem
Context triple: [Helly’s theorem, relatedTo, Tverberg’s theorem]

• A. Helly’s theorem
  Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
• B. Radon’s theorem
  Radon’s theorem is a fundamental result in convex geometry stating that any set of sufficiently many points in Euclidean space can be partitioned into two disjoint subsets whose convex hulls intersect.
• C. Carathéodory’s theorem in convex geometry
  Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
• D. Borsuk’s conjecture in geometry
  Borsuk’s conjecture in geometry is a famous (now disproven in higher dimensions) problem in metric geometry that proposed any bounded set in n-dimensional Euclidean space can be partitioned into n+1 subsets of smaller diameter.
• E. Sylvester–Gallai theorem
  The Sylvester–Gallai theorem is a result in incidence geometry stating that for any finite set of points in the Euclidean plane not all on a single line, there exists a line that passes through exactly two of the points.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Tverberg’s theorem
Target entity description: Tverberg’s theorem is a fundamental result in combinatorial geometry that guarantees any sufficiently large set of points in Euclidean space can be partitioned into subsets whose convex hulls all intersect.

• A. Helly’s theorem
  Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
• B. Radon’s theorem
  Radon’s theorem is a fundamental result in convex geometry stating that any set of sufficiently many points in Euclidean space can be partitioned into two disjoint subsets whose convex hulls intersect.
• C. Carathéodory’s theorem in convex geometry
  Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
• D. Borsuk’s conjecture in geometry
  Borsuk’s conjecture in geometry is a famous (now disproven in higher dimensions) problem in metric geometry that proposed any bounded set in n-dimensional Euclidean space can be partitioned into n+1 subsets of smaller diameter.
• E. Sylvester–Gallai theorem
  The Sylvester–Gallai theorem is a result in incidence geometry stating that for any finite set of points in the Euclidean plane not all on a single line, there exists a line that passes through exactly two of the points.
• F. None of above. chosen