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: Birkhoff–von Neumann theorem | Statement: [Garrett Birkhoff, notableConcept, Birkhoff–von Neumann theorem]

Target entity: Birkhoff–von Neumann theorem
Context triple: [Garrett Birkhoff, notableConcept, Birkhoff–von Neumann theorem]

• A. 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.
• B. Gleason’s theorem
  Gleason’s theorem is a foundational result in the mathematical formulation of quantum mechanics that characterizes all probability measures on the lattice of projection operators in a Hilbert space, effectively justifying the Born rule.
• C. de Bruijn–van Aardenne–Ehrenfest theorem
  The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
• D. Gelfand–Naimark theorem
  The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
• 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: Birkhoff–von Neumann theorem
Triple: [Garrett Birkhoff, notableConcept, Birkhoff–von Neumann theorem]

The Birkhoff–von Neumann theorem is a fundamental result in matrix theory and combinatorics stating that every doubly stochastic matrix can be expressed as a convex combination of permutation matrices.

Target entity: Birkhoff–von Neumann theorem
Target entity description: The Birkhoff–von Neumann theorem is a fundamental result in matrix theory and combinatorics stating that every doubly stochastic matrix can be expressed as a convex combination of permutation matrices.

• A. 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.
• B. Gleason’s theorem
  Gleason’s theorem is a foundational result in the mathematical formulation of quantum mechanics that characterizes all probability measures on the lattice of projection operators in a Hilbert space, effectively justifying the Born rule.
• C. de Bruijn–van Aardenne–Ehrenfest theorem
  The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
• D. Gelfand–Naimark theorem
  The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
• 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