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: Weaver’s conjecture | Statement: [Bourgain–Tzafriri restricted invertibility principle, relatedTo, Weaver’s conjecture]

Target entity: Weaver’s conjecture
Context triple: [Bourgain–Tzafriri restricted invertibility principle, relatedTo, Weaver’s conjecture]

• A. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• B. Conway's thrackle conjecture
  Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
• C. Conway's 99-graph problem
  Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
• D. König's theorem in graph theory
  König's theorem in graph theory is a fundamental result in bipartite graphs stating that the size of a maximum matching equals the size of a minimum vertex cover.
• E. Menger theorem in graph theory
  Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Weaver’s conjecture
Target entity description: Weaver’s conjecture is a problem in functional analysis and operator theory concerning the partitioning of vectors in Hilbert spaces, whose resolution by Marcus, Spielman, and Srivastava led to a proof of the Kadison–Singer problem.

• A. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• B. Conway's thrackle conjecture
  Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
• C. Conway's 99-graph problem
  Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
• D. König's theorem in graph theory
  König's theorem in graph theory is a fundamental result in bipartite graphs stating that the size of a maximum matching equals the size of a minimum vertex cover.
• E. Menger theorem in graph theory
  Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
• F. None of above. chosen