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: Gauss–Bonnet theorem | Statement: [Gauss–Bonnet theorem (early form), historicalFormOf, Gauss–Bonnet theorem]

Target entity: Gauss–Bonnet theorem
Context triple: [Gauss–Bonnet theorem (early form), historicalFormOf, Gauss–Bonnet theorem]

• A. Gauss–Bonnet theorem (early form) chosen
  The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
• B. Theorema Egregium
  Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
• C. Gaussian curvature
  Gaussian curvature is a fundamental concept in differential geometry that measures how a surface bends at a point by combining its principal curvatures into a single intrinsic quantity.
• D. Poincaré–Hopf theorem
  The Poincaré–Hopf theorem is a fundamental result in differential topology that relates the sum of the indices of a vector field’s isolated zeros on a compact manifold to the manifold’s Euler characteristic.
• E. Nash embedding theorem
  The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: historicalFormOf
Context triple: [Gauss–Bonnet theorem (early form), historicalFormOf, Gauss–Bonnet theorem]

• A. historicalForm chosen
  Indicates that one entity is an earlier or historically attested form or variant of another entity.
• B. historicallyRecognizedAs
  Indicates that an entity has been acknowledged or designated under a particular name, status, or role during a past historical period.
• C. historicallyBorneBy
  Indicates that an entity has carried, possessed, or used another entity (such as a name, title, or symbol) at some point in the past.
• D. historicalFormation
  Indicates the process or circumstances through which something came into existence or took shape over time in history.
• E. hasHistoricalOrigin
  Indicates that something originated, was first established, or came into existence during a specific historical period or context.
• F. None of above.