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, sharpnessWitnessedBy, Koebe function]

Target entity: Koebe function
Context triple: [Koebe quarter theorem, sharpnessWitnessedBy, 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. Schwarz–Pick theorem
  The Schwarz–Pick theorem is a fundamental result in complex analysis that characterizes holomorphic self-maps of the unit disk by showing they are distance-decreasing with respect to the hyperbolic (Poincaré) metric.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

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

• A. sharpnessCondition
  Indicates the condition or degree of sharpness that something possesses or is required to have.
• B. isSeeOf
  Indicates that one entity serves as the episcopal or ecclesiastical seat (see) of another, typically a bishop or similar religious office.
• C. sharpeningType
  Indicates the method or style by which something is sharpened or made sharper.
• D. hasSharperPeakThan
  Indicates that one entity’s peak (e.g., in a graph, distribution, or signal) is more pointed or narrow than the peak of another entity.
• E. visibleAt
  Indicates that one entity can be seen or perceived from a specific location, viewpoint, or context at a given time.
• F. None of above. chosen