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: Koebe function | Statement: [Koebe quarter theorem, extremalFunction, Koebe function]

Target entity: Koebe function
Context triple: [Koebe quarter theorem, extremalFunction, Koebe function]

• A. Koebe function chosen
  The Koebe function is a specific univalent holomorphic function on the unit disk that extremizes several classical bounds in geometric function theory, notably serving as the extremal example in the Koebe quarter theorem.
• B. Koebe quarter theorem
  The Koebe quarter theorem is a fundamental result in complex analysis stating that any univalent holomorphic function on the unit disk maps it onto a domain containing a disk of radius one quarter, providing a sharp bound on the size of the image.
• C. Bieberbach conjecture
  The Bieberbach conjecture, now a theorem, is a landmark result in complex analysis that characterizes the size of Taylor coefficients of normalized univalent (injective) holomorphic functions on the unit disk.
• D. Riemann mapping theorem
  The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
• E. Schwarz lemma
  Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: extremalFunction
Context triple: [Koebe quarter theorem, extremalFunction, Koebe function]

• A. isExtremalWhen
  Indicates that a given entity or configuration attains an extreme value (such as a maximum or minimum) of some specified quantity or property under certain conditions.
• B. hasExtremePoint
  Indicates that one entity possesses or includes another entity that is an extreme (e.g., maximum or minimum) point within its structure or boundary.
• C. EuclideanFunction
  Indicates a relationship defined by a Euclidean distance–based function, typically mapping entities or their attributes to values derived from Euclidean metric properties.
• D. hasAsymptotics
  Indicates that one entity describes or determines the asymptotic behavior or growth rate of another entity, typically in a limiting or large-scale sense.
• E. functionalEquationPartProvedBy
  Indicates that a specific part or component of a functional equation has been proven or established by a particular proof, method, or agent.
• F. None of above. chosen