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: Banach–Tarski-type decompositions | Statement: [von Neumann paradox in set theory, isAbstractVersionOf, Banach–Tarski-type decompositions]

Target entity: Banach–Tarski-type decompositions
Context triple: [von Neumann paradox in set theory, isAbstractVersionOf, Banach–Tarski-type decompositions]

• A. Ulam problem in set theory
  The Ulam problem in set theory is a well-known question posed by Stanislaw Ulam concerning the structure and properties of measurable sets and functions, particularly in relation to homomorphisms and measure-theoretic regularity.
• B. Israel–Carter–Robinson uniqueness theorems
  The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
• C. von Neumann paradox in set theory chosen
  The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
• D. Khinchin–Kahane type inequalities
  Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
• E. Euler’s polyhedron formula
  Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: isAbstractVersionOf
Context triple: [von Neumann paradox in set theory, isAbstractVersionOf, Banach–Tarski-type decompositions]

• A. isVersionOf
  Indicates that one entity is a particular version, edition, or variant derived from another entity.
• B. isBaseFor
  Indicates that one entity serves as the foundational support, starting point, or underlying basis upon which another entity is built, developed, or depends.
• C. isBasedOn
  Indicates that one entity is derived from, inspired by, or developed using the content, structure, or principles of another entity.
• D. wasSupersededBy
  Indicates that one entity has been replaced or made obsolete by another entity that takes over its role or function.
• E. inheritedFrom
  Indicates that one entity has received or derived something (such as traits, rights, or property) from another entity, typically a predecessor or ancestor.
• F. None of above. chosen