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: Doignon’s theorem | Statement: [Helly’s theorem, hasVariant, Doignon’s theorem]

Target entity: Doignon’s theorem
Context triple: [Helly’s theorem, hasVariant, Doignon’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. Low’s theorem
  Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
• D. Szekeres–Lindström theorem
  The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
• E. Jarník–Besicovitch theorem
  The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Doignon’s theorem
Target entity description: Doignon’s theorem is a discrete analogue of Helly’s theorem that characterizes when a family of convex sets in Euclidean space has an integer point in common based on the intersections of small subfamilies.

• 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. Low’s theorem
  Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
• D. Szekeres–Lindström theorem
  The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
• E. Jarník–Besicovitch theorem
  The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
• F. None of above. chosen