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: Kolmogorov’s invariant torus theorem | Statement: [Kolmogorov–Arnold–Moser theory, relatedTo, Kolmogorov’s invariant torus theorem]

Target entity: Kolmogorov’s invariant torus theorem
Context triple: [Kolmogorov–Arnold–Moser theory, relatedTo, Kolmogorov’s invariant torus theorem]

• A. Kolmogorov–Arnold–Moser theory chosen
  Kolmogorov–Arnold–Moser theory is a fundamental result in dynamical systems that explains the persistence of quasi-periodic motions in nearly integrable Hamiltonian systems under small perturbations.
• B. Liouville–Arnold theorem
  The Liouville–Arnold theorem is a fundamental result in Hamiltonian mechanics that guarantees the integrability of a system with sufficiently many conserved quantities and describes its motion as quasi-periodic on invariant tori in phase space.
• C. Poincaré–Birkhoff fixed-point theorem
  The Poincaré–Birkhoff fixed-point theorem is a fundamental result in dynamical systems and topology that guarantees the existence of at least two fixed points for certain area-preserving twist maps of an annulus.
• D. Kakutani equivalence in ergodic theory
  Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
• E. Godbillon–Vey invariant
  The Godbillon–Vey invariant is a characteristic class in differential topology that assigns a real number to certain codimension-one foliations of manifolds, capturing subtle geometric and dynamical properties of their leaf structure.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.