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 paradox | Statement: [Stefan Banach, eponymOf, Banach–Tarski paradox]

Target entity: Banach–Tarski paradox
Context triple: [Stefan Banach, eponymOf, Banach–Tarski paradox]

• A. Banach–Tarski paradox chosen
  The Banach–Tarski paradox is a theorem in set-theoretic geometry stating that a solid ball in 3‑dimensional space can be decomposed into finitely many non-measurable pieces and reassembled into two identical copies of the original ball, highlighting counterintuitive consequences of the axiom of choice.
• B. Steinhaus theorem
  The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
• C. Banach–Mazur theorem
  The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
• D. Brouwer fixed-point theorem
  The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
• E. Smale’s paradox
  Smale’s paradox is a result in differential topology showing that a sphere can be turned inside out in three-dimensional space through smooth deformations without tearing or creasing, challenging intuitive notions of geometry.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.