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: Riemann sphere | Statement: [Fuchsian differential equation, oftenConsideredOn, Riemann sphere]

Target entity: Riemann sphere
Context triple: [Fuchsian differential equation, oftenConsideredOn, Riemann sphere]

• A. Riemann sphere chosen
  The Riemann sphere is the complex plane plus a point at infinity, forming a one-dimensional complex manifold topologically equivalent to a sphere and used to study meromorphic functions and complex analysis.
• B. Möbius transformations
  Möbius transformations are conformal automorphisms of the extended complex plane represented by fractional linear functions that map circles and lines to circles and lines.
• C. Poincaré disk model
  The Poincaré disk model is a representation of hyperbolic geometry in which the entire infinite hyperbolic plane is mapped inside a unit disk, with geodesics appearing as circular arcs orthogonal to the boundary.
• D. Poincaré upper half-plane model
  The Poincaré upper half-plane model is a standard representation of the hyperbolic plane using the complex numbers with positive imaginary part, equipped with a specific metric that makes geodesics appear as semicircles and vertical lines.
• 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: oftenConsideredOn
Context triple: [Fuchsian differential equation, oftenConsideredOn, Riemann sphere]

• A. consideredIn chosen
  Indicates that one entity is taken into account, examined, or included as a factor within the context, scope, or decision framework of another entity.
• B. nowConsidered
  Indicates that something has come to be regarded or classified in a particular way at the present time, possibly differing from how it was regarded before.
• C. considered
  Indicates that one entity regards, judges, or thinks about another entity in a particular way or context.
• D. couldConsider
  Indicates that one entity has the potential or option to take another entity into account when making a decision, judgment, or evaluation.
• E. onceConsideredCloseTo
  Indicates that two entities were previously regarded as having a close or intimate relationship, but that closeness is no longer current or assumed.
• F. None of above.