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: Pfaffian systems | Statement: [Pfaffian form, usedIn, Pfaffian systems]

Target entity: Pfaffian systems
Context triple: [Pfaffian form, usedIn, Pfaffian systems]

• A. 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.
• B. Carathéodory–Jacobi–Lie theorem
  The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
• C. 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.
• D. Picard–Vessiot theory
  Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
• E. Poisson geometry
  Poisson geometry is the branch of differential geometry that studies manifolds equipped with a Poisson bracket, generalizing classical Hamiltonian mechanics and symplectic geometry.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Pfaffian systems
Target entity description: 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.

• A. 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.
• B. Carathéodory–Jacobi–Lie theorem
  The Carathéodory–Jacobi–Lie theorem is a fundamental result in symplectic geometry and Hamiltonian mechanics that provides canonical local coordinates adapted to a given set of commuting functions.
• C. 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.
• D. Picard–Vessiot theory
  Picard–Vessiot theory is a branch of differential Galois theory that studies linear differential equations via the symmetries of their solution fields, analogous to classical Galois theory for polynomial equations.
• E. Poisson geometry
  Poisson geometry is the branch of differential geometry that studies manifolds equipped with a Poisson bracket, generalizing classical Hamiltonian mechanics and symplectic geometry.
• F. None of above. chosen