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: Cartan’s method of equivalence | Statement: [theory of G-structures, relatedTo, Cartan’s method of equivalence]

Target entity: Cartan’s method of equivalence
Context triple: [theory of G-structures, relatedTo, Cartan’s method of equivalence]

• A. Pfaffian systems
  Pfaffian systems are collections of first-order differential equations expressed in terms of differential 1-forms that define geometric structures and constraints on manifolds in differential geometry and control theory.
• B. Vessiot theory of differential equations
  The Vessiot theory of differential equations is a geometric framework that studies differential equations via their symmetry and structure using concepts from Lie groups and differential geometry.
• C. Cartan connections
  Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
• D. theory of G-structures
  The theory of G-structures is a framework in differential geometry that studies geometric structures on manifolds defined by reductions of the frame bundle to a Lie group G, encompassing and unifying many classical geometries such as Riemannian, symplectic, and complex structures.
• E. Oka–Cartan theory
  Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Cartan’s method of equivalence
Target entity description: Cartan’s method of equivalence is a geometric technique that uses differential forms and moving frames to determine when two geometric structures are locally the same up to a suitable transformation group.

• A. Pfaffian systems
  Pfaffian systems are collections of first-order differential equations expressed in terms of differential 1-forms that define geometric structures and constraints on manifolds in differential geometry and control theory.
• B. Vessiot theory of differential equations
  The Vessiot theory of differential equations is a geometric framework that studies differential equations via their symmetry and structure using concepts from Lie groups and differential geometry.
• C. Cartan connections
  Cartan connections are a geometric framework generalizing affine and Riemannian connections that model curved spaces on homogeneous spaces, developed by Élie Cartan.
• D. theory of G-structures chosen
  The theory of G-structures is a framework in differential geometry that studies geometric structures on manifolds defined by reductions of the frame bundle to a Lie group G, encompassing and unifying many classical geometries such as Riemannian, symplectic, and complex structures.
• E. Oka–Cartan theory
  Oka–Cartan theory is a foundational area of complex analysis that studies the structure and properties of holomorphic functions and coherent analytic sheaves on complex manifolds, particularly Stein spaces.
• F. None of above.