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: non-Euclidean geometry | Statement: [Maurice Princet, usedConcept, non-Euclidean geometry]

Target entity: non-Euclidean geometry
Context triple: [Maurice Princet, usedConcept, non-Euclidean geometry]

• A. Non-Euclidean Geometry chosen
  Non-Euclidean Geometry is a branch of mathematics that studies geometrical systems in which Euclid’s parallel postulate does not hold, leading to alternative models of space such as hyperbolic and elliptic geometry.
• B. Euclidean geometry
  Euclidean geometry is the classical mathematical system that studies flat space and shapes using axioms about points, lines, and angles, forming the foundation of much of traditional mathematics and physics.
• C. Lorentzian geometry
  Lorentzian geometry is the branch of differential geometry that studies manifolds equipped with metrics of Lorentzian signature, providing the mathematical framework for general relativity and spacetime physics.
• D. Möbius geometry
  Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
• E. On the Principles of Geometry
  "On the Principles of Geometry" is Nikolai Lobachevsky’s foundational work that introduced non-Euclidean (hyperbolic) geometry, challenging the universality of Euclid’s parallel postulate.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.