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: Weierstrass approximation theorem | Statement: [Bernstein polynomials, associatedWithTheorem, Weierstrass approximation theorem]

Target entity: Weierstrass approximation theorem
Context triple: [Bernstein polynomials, associatedWithTheorem, Weierstrass approximation theorem]

• A. Weierstrass approximation theorem chosen
  The Weierstrass approximation theorem is a fundamental result in real analysis stating that any continuous function on a closed interval can be uniformly approximated by polynomials.
• B. Stone–Weierstrass theorem
  The Stone–Weierstrass theorem is a fundamental result in functional analysis that characterizes when a subalgebra of continuous functions on a compact space is dense, thereby generalizing classical polynomial approximation results.
• C. Chebyshev alternation theorem
  The Chebyshev alternation theorem is a fundamental result in approximation theory that characterizes the best uniform (minimax) polynomial approximation to a continuous function by the presence of alternating maximum errors at a finite set of points.
• D. Mergelyan's theorem
  Mergelyan's theorem is a fundamental result in complex analysis stating that every function continuous on a compact subset of the complex plane with connected complement and holomorphic in its interior can be uniformly approximated by polynomials.
• E. Runge approximation theorem
  The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: associatedWithTheorem
Context triple: [Bernstein polynomials, associatedWithTheorem, Weierstrass approximation theorem]

• A. relatedTheorem
  Indicates that one theorem is connected to another through a logical, thematic, or derivational relationship.
• B. hasTheorem chosen
  Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
• C. associatedConjecture
  Indicates that one entity is linked or connected to a particular conjecture, typically as its subject, source, or relevant context.
• D. hasTheoremNamedAfter
  Indicates that a theorem is named in honor of or after a particular person or entity.
• E. relatedConjecture
  Indicates that one conjecture is connected or associated with another conjecture, such as by similarity, dependency, or thematic relation.
• F. None of above.